hypothesis examples about education

• Resources Home 🏠
• Try SciSpace Copilot
• Search research papers
• Add Copilot Extension
• Try AI Detector
• Try Paraphraser
• Try Citation Generator
• April Papers
• June Papers
• July Papers

The Craft of Writing a Strong Hypothesis

Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good  alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

• Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
• Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher  the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

• A research hypothesis has to be simple yet clear to look justifiable enough.
• It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
• It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
• A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
• If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
• A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

You might also like

Consensus GPT vs. SciSpace GPT: Choose the Best GPT for Research

Literature Review and Theoretical Framework: Understanding the Differences

Types of Essays in Academic Writing - Quick Guide (2024)

• How it works

Published by Nicolas at January 16th, 2024 , Revised On January 23, 2024

How To Write A Hypotheses – Guide For Students

The word “hypothesis” might conjure up images of scientists in white coats, but crafting a solid hypothesis is a crucial skill for students in any field. Whether you are analyzing Shakespeare’s sonnets or conducting a science experiment, a well-defined research hypothesis sets the stage for your dissertation or thesis and fuels your investigation. 

Table of Contents

Writing a hypothesis is a crucial step in the research process. A hypothesis serves as the foundation of your research paper because it guides the direction of your study and provides a clear framework for investigation. But how to write a hypothesis? This blog will help you craft one. Let’s get started.

What Is A Hypothesis

A hypothesis is a clear and testable thesis statement or prediction that serves as the foundation of a research study. It is formulated based on existing knowledge, observations, and theoretical frameworks. 

A hypothesis articulates the researcher’s expectations regarding the relationship between variables in a study.

Hypothesis Example

Students exposed to multimedia-enhanced teaching methods will demonstrate higher retention of information compared to those taught using traditional methods.

The formulation of a hypothesis is crucial for guiding the research process and providing a clear direction for data collection and analysis. A well-crafted research hypothesis not only makes the research purpose explicit but also sets the stage for drawing meaningful conclusions from the study’s findings.

What Is A Null Hypothesis And Alternative Hypothesis

There are two main types of hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1 or Ha). 

The null hypothesis posits that there is no significant effect or relationship, while the alternative hypothesis suggests the presence of a significant effect or relationship.

For example, in a study investigating the effect of a new drug on blood pressure, the null hypothesis might state that there is no difference in blood pressure between the control group (not receiving the drug) and the experimental group (receiving the drug). The alternative hypothesis, on the other hand, would propose that there is a significant difference in blood pressure between the two groups.

The literature review we write have:

• Precision and Clarity
• Zero Plagiarism
• High-level Encryption
• Authentic Sources

How To Write A Good Research Hypothesis

Writing a hypothesis involves a systematic process that guides your research and provides a clear and testable statement about the expected relationship between variables. Go through the MLA vs. APA guidelines before writing. Here are the steps to help you how to write a hypothesis:

Step 1: Identify The Research Topic

Clearly define the research topic or question that you want to investigate. Ensure that your research question is specific and focused, providing a clear direction for your study.

Step 2: Conduct A Literature Review

Review existing literature related to your research topic. A thorough literature review helps you understand what is already known in the field, identify gaps, and build a foundation for formulating your hypothesis.

Step 3: Define Variables

Identify the variables involved in your study. The independent variable is the factor you manipulate, and the dependent variable is the one you measure. Clearly define the characteristics or conditions you are studying.

Step 4: Establish The Relationship

Determine the expected relationship between the independent and dependent variables. Will a change in the independent variable lead to a change in the dependent variable? Specify whether you anticipate a positive, negative, or no relationship.

Step 5: Formulate The Null Hypothesis (H0)

The null hypothesis represents the default position, suggesting that there is no significant effect or relationship between the variables you are studying. It serves as the baseline to be tested against. The null hypothesis is often denoted as H0.

Step 6: Formulate The Alternative Hypothesis (H1 or Ha)

The alternative hypothesis articulates the researcher’s expectation about the existence of a significant effect or relationship. It is what you aim to support with your research paper . The alternative hypothesis is denoted as H1 or Ha.

For example, if your research topic is about the effect of a new fertilizer on plant growth:

• Null Hypothesis (H0): There is no significant difference in plant growth between plants treated with the traditional fertilizer and those treated with the new fertilizer.
• Alternative Hypothesis (H1): There is a significant difference in plant growth between plants treated with the traditional fertilizer and those treated with the new fertilizer.

Step 7: Ensure Testability And Specificity

Confirm that your research hypothesis is testable and can be empirically investigated. Ensure that it is specific, providing a clear and measurable statement that can be validated or refuted through data collection and analysis.

Hypothesis Examples

What makes a good hypothesis.

• Clear Statement: A hypothesis should be stated clearly and precisely. It should be easily understandable and convey the expected relationship between variables.
• Testability: A hypothesis must be testable through empirical observation or experimentation. This means that there should be a feasible way to collect data and assess whether the expected relationship holds true.
• Specificity: The research hypothesis should be specific in terms of the variables involved and the nature of the expected relationship. Vague or ambiguous hypotheses can lead to unclear research outcomes.
• Measurability: Variables in a hypothesis should be measurable, meaning they can be quantified or observed objectively. This ensures that the research can be conducted with precision.
• Falsifiability: A good research hypothesis should be falsifiable, meaning there should be a possibility of proving it wrong. This concept is fundamental to the scientific method, as hypotheses that cannot be tested or disproven lack scientific validity.

Frequently Asked Questions

How to write a hypothesis.

• Clearly state the research question.
• Identify the variables involved.
• Formulate a clear and testable prediction.
• Use specific and measurable terms.
• Align the hypothesis with the research question.
• Distinguish between the null hypothesis (no effect) and alternative hypothesis (expected effect).
• Ensure the hypothesis is falsifiable and subject to empirical testing.

How to write a hypothesis for a lab?

• Identify the purpose of the lab.
• Clearly state the relationship between variables.
• Use concise language and specific terms.
• Make the hypothesis testable through experimentation.
• Align with the lab’s objectives.
• Include an if-then statement to express the expected outcome.
• Ensure clarity and relevance to the experimental setup.

What Is A Null Hypothesis?

A null hypothesis is a statement suggesting no effect or relationship between variables in a research study. It serves as the default assumption, stating that any observed differences or effects are due to chance. Researchers aim to reject the null hypothesis based on statistical evidence to support their alternative hypothesis.

How to write a null hypothesis?

• State there is no effect, difference, or relationship between variables.
• Use clear and specific language.
• Frame it in a testable manner.
• Align with the research question.
• Specify parameters for statistical testing.
• Consider it as the default assumption to be tested and potentially rejected in favour of the alternative hypothesis.

What is the p-value of a hypothesis test?

The p-value in a hypothesis test represents the probability of obtaining observed results, or more extreme ones, if the null hypothesis is true. A lower p-value suggests stronger evidence against the null hypothesis, often leading to its rejection. Common significance thresholds include 0.05 or 0.01.

How to write a hypothesis in science?

• Clearly state the research question
• Identify the variables and their relationship.
• Formulate a testable and falsifiable prediction.
• Use specific, measurable terms.
• Distinguish between the null and alternative hypotheses.
• Ensure clarity and relevance to the scientific investigation.

How to write a hypothesis for a research proposal?

• Clearly define the research question.
• Identify variables and their expected relationship.
• Formulate a specific, testable hypothesis.
• Align the hypothesis with the proposal’s objectives.
• Clearly articulate the null hypothesis.
• Use concise language and measurable terms.
• Ensure the hypothesis aligns with the proposed research methodology.

How to write a good hypothesis psychology?

• Formulate a specific and testable prediction.
• Use precise and measurable terms.
• Align the hypothesis with psychological theories.
• Articulate the null hypothesis.
• Ensure the hypothesis guides empirical testing in psychological research.

You May Also Like

Learn how to write an exceptional research paper with the help of professionally crafted research paper examples. Become an expert now!

This blog comprehensively assigns what the cognitive failures questionnaire measures. Read more to get the complete information.

Learn everything about meta synthesis literature review in this comprehensive guide. From definition and process to its types and challenges.

Ready to place an order?

USEFUL LINKS

Learning resources, company details.

• How It Works

Automated page speed optimizations for fast site performance

Choose Your Test

Sat / act prep online guides and tips, what is a hypothesis and how do i write one.

General Education

Think about something strange and unexplainable in your life. Maybe you get a headache right before it rains, or maybe you think your favorite sports team wins when you wear a certain color. If you wanted to see whether these are just coincidences or scientific fact, you would form a hypothesis, then create an experiment to see whether that hypothesis is true or not.

But what is a hypothesis, anyway? If you’re not sure about what a hypothesis is--or how to test for one!--you’re in the right place. This article will teach you everything you need to know about hypotheses, including: 

• Defining the term “hypothesis” 
• Providing hypothesis examples 
• Giving you tips for how to write your own hypothesis

So let’s get started!

What Is a Hypothesis?

Merriam Webster defines a hypothesis as “an assumption or concession made for the sake of argument.” In other words, a hypothesis is an educated guess . Scientists make a reasonable assumption--or a hypothesis--then design an experiment to test whether it’s true or not. Keep in mind that in science, a hypothesis should be testable. You have to be able to design an experiment that tests your hypothesis in order for it to be valid. 

As you could assume from that statement, it’s easy to make a bad hypothesis. But when you’re holding an experiment, it’s even more important that your guesses be good...after all, you’re spending time (and maybe money!) to figure out more about your observation. That’s why we refer to a hypothesis as an educated guess--good hypotheses are based on existing data and research to make them as sound as possible.

Hypotheses are one part of what’s called the scientific method .  Every (good) experiment or study is based in the scientific method. The scientific method gives order and structure to experiments and ensures that interference from scientists or outside influences does not skew the results. It’s important that you understand the concepts of the scientific method before holding your own experiment. Though it may vary among scientists, the scientific method is generally made up of six steps (in order):

• Observation
• Asking questions
• Forming a hypothesis
• Analyze the data
• Communicate your results

You’ll notice that the hypothesis comes pretty early on when conducting an experiment. That’s because experiments work best when they’re trying to answer one specific question. And you can’t conduct an experiment until you know what you’re trying to prove!

Independent and Dependent Variables 

After doing your research, you’re ready for another important step in forming your hypothesis: identifying variables. Variables are basically any factor that could influence the outcome of your experiment . Variables have to be measurable and related to the topic being studied.

There are two types of variables:  independent variables and dependent variables. I ndependent variables remain constant . For example, age is an independent variable; it will stay the same, and researchers can look at different ages to see if it has an effect on the dependent variable. 

Speaking of dependent variables... dependent variables are subject to the influence of the independent variable , meaning that they are not constant. Let’s say you want to test whether a person’s age affects how much sleep they need. In that case, the independent variable is age (like we mentioned above), and the dependent variable is how much sleep a person gets. 

Variables will be crucial in writing your hypothesis. You need to be able to identify which variable is which, as both the independent and dependent variables will be written into your hypothesis. For instance, in a study about exercise, the independent variable might be the speed at which the respondents walk for thirty minutes, and the dependent variable would be their heart rate. In your study and in your hypothesis, you’re trying to understand the relationship between the two variables.

Elements of a Good Hypothesis

The best hypotheses start by asking the right questions . For instance, if you’ve observed that the grass is greener when it rains twice a week, you could ask what kind of grass it is, what elevation it’s at, and if the grass across the street responds to rain in the same way. Any of these questions could become the backbone of experiments to test why the grass gets greener when it rains fairly frequently.

As you’re asking more questions about your first observation, make sure you’re also making more observations . If it doesn’t rain for two weeks and the grass still looks green, that’s an important observation that could influence your hypothesis. You'll continue observing all throughout your experiment, but until the hypothesis is finalized, every observation should be noted.

Finally, you should consult secondary research before writing your hypothesis . Secondary research is comprised of results found and published by other people. You can usually find this information online or at your library. Additionally, m ake sure the research you find is credible and related to your topic. If you’re studying the correlation between rain and grass growth, it would help you to research rain patterns over the past twenty years for your county, published by a local agricultural association. You should also research the types of grass common in your area, the type of grass in your lawn, and whether anyone else has conducted experiments about your hypothesis. Also be sure you’re checking the quality of your research . Research done by a middle school student about what minerals can be found in rainwater would be less useful than an article published by a local university.

Writing Your Hypothesis

Once you’ve considered all of the factors above, you’re ready to start writing your hypothesis. Hypotheses usually take a certain form when they’re written out in a research report.

When you boil down your hypothesis statement, you are writing down your best guess and not the question at hand . This means that your statement should be written as if it is fact already, even though you are simply testing it.

The reason for this is that, after you have completed your study, you'll either accept or reject your if-then or your null hypothesis. All hypothesis testing examples should be measurable and able to be confirmed or denied. You cannot confirm a question, only a statement! 

In fact, you come up with hypothesis examples all the time! For instance, when you guess on the outcome of a basketball game, you don’t say, “Will the Miami Heat beat the Boston Celtics?” but instead, “I think the Miami Heat will beat the Boston Celtics.” You state it as if it is already true, even if it turns out you’re wrong. You do the same thing when writing your hypothesis.

Additionally, keep in mind that hypotheses can range from very specific to very broad.  These hypotheses can be specific, but if your hypothesis testing examples involve a broad range of causes and effects, your hypothesis can also be broad.  

The Two Types of Hypotheses

Now that you understand what goes into a hypothesis, it’s time to look more closely at the two most common types of hypothesis: the if-then hypothesis and the null hypothesis.

#1: If-Then Hypotheses

First of all, if-then hypotheses typically follow this formula:

If ____ happens, then ____ will happen.

The goal of this type of hypothesis is to test the causal relationship between the independent and dependent variable. It’s fairly simple, and each hypothesis can vary in how detailed it can be. We create if-then hypotheses all the time with our daily predictions. Here are some examples of hypotheses that use an if-then structure from daily life: 

• If I get enough sleep, I’ll be able to get more work done tomorrow.
• If the bus is on time, I can make it to my friend’s birthday party. 
• If I study every night this week, I’ll get a better grade on my exam. 

In each of these situations, you’re making a guess on how an independent variable (sleep, time, or studying) will affect a dependent variable (the amount of work you can do, making it to a party on time, or getting better grades). 

You may still be asking, “What is an example of a hypothesis used in scientific research?” Take one of the hypothesis examples from a real-world study on whether using technology before bed affects children’s sleep patterns. The hypothesis read s:

“We hypothesized that increased hours of tablet- and phone-based screen time at bedtime would be inversely correlated with sleep quality and child attention.”

It might not look like it, but this is an if-then statement. The researchers basically said, “If children have more screen usage at bedtime, then their quality of sleep and attention will be worse.” The sleep quality and attention are the dependent variables and the screen usage is the independent variable. (Usually, the independent variable comes after the “if” and the dependent variable comes after the “then,” as it is the independent variable that affects the dependent variable.) This is an excellent example of how flexible hypothesis statements can be, as long as the general idea of “if-then” and the independent and dependent variables are present.

#2: Null Hypotheses

Your if-then hypothesis is not the only one needed to complete a successful experiment, however. You also need a null hypothesis to test it against. In its most basic form, the null hypothesis is the opposite of your if-then hypothesis . When you write your null hypothesis, you are writing a hypothesis that suggests that your guess is not true, and that the independent and dependent variables have no relationship .

One null hypothesis for the cell phone and sleep study from the last section might say: 

“If children have more screen usage at bedtime, their quality of sleep and attention will not be worse.” 

In this case, this is a null hypothesis because it’s asking the opposite of the original thesis! 

Conversely, if your if-then hypothesis suggests that your two variables have no relationship, then your null hypothesis would suggest that there is one. So, pretend that there is a study that is asking the question, “Does the amount of followers on Instagram influence how long people spend on the app?” The independent variable is the amount of followers, and the dependent variable is the time spent. But if you, as the researcher, don’t think there is a relationship between the number of followers and time spent, you might write an if-then hypothesis that reads:

“If people have many followers on Instagram, they will not spend more time on the app than people who have less.”

In this case, the if-then suggests there isn’t a relationship between the variables. In that case, one of the null hypothesis examples might say:

“If people have many followers on Instagram, they will spend more time on the app than people who have less.”

You then test both the if-then and the null hypothesis to gauge if there is a relationship between the variables, and if so, how much of a relationship. 

4 Tips to Write the Best Hypothesis

If you’re going to take the time to hold an experiment, whether in school or by yourself, you’re also going to want to take the time to make sure your hypothesis is a good one. The best hypotheses have four major elements in common: plausibility, defined concepts, observability, and general explanation.

#1: Plausibility

At first glance, this quality of a hypothesis might seem obvious. When your hypothesis is plausible, that means it’s possible given what we know about science and general common sense. However, improbable hypotheses are more common than you might think. 

Imagine you’re studying weight gain and television watching habits. If you hypothesize that people who watch more than  twenty hours of television a week will gain two hundred pounds or more over the course of a year, this might be improbable (though it’s potentially possible). Consequently, c ommon sense can tell us the results of the study before the study even begins.

Improbable hypotheses generally go against  science, as well. Take this hypothesis example: 

“If a person smokes one cigarette a day, then they will have lungs just as healthy as the average person’s.” 

This hypothesis is obviously untrue, as studies have shown again and again that cigarettes negatively affect lung health. You must be careful that your hypotheses do not reflect your own personal opinion more than they do scientifically-supported findings. This plausibility points to the necessity of research before the hypothesis is written to make sure that your hypothesis has not already been disproven.

#2: Defined Concepts

The more advanced you are in your studies, the more likely that the terms you’re using in your hypothesis are specific to a limited set of knowledge. One of the hypothesis testing examples might include the readability of printed text in newspapers, where you might use words like “kerning” and “x-height.” Unless your readers have a background in graphic design, it’s likely that they won’t know what you mean by these terms. Thus, it’s important to either write what they mean in the hypothesis itself or in the report before the hypothesis.

Here’s what we mean. Which of the following sentences makes more sense to the common person?

If the kerning is greater than average, more words will be read per minute.

If the space between letters is greater than average, more words will be read per minute.

For people reading your report that are not experts in typography, simply adding a few more words will be helpful in clarifying exactly what the experiment is all about. It’s always a good idea to make your research and findings as accessible as possible. 

Good hypotheses ensure that you can observe the results. 

#3: Observability

In order to measure the truth or falsity of your hypothesis, you must be able to see your variables and the way they interact. For instance, if your hypothesis is that the flight patterns of satellites affect the strength of certain television signals, yet you don’t have a telescope to view the satellites or a television to monitor the signal strength, you cannot properly observe your hypothesis and thus cannot continue your study.

Some variables may seem easy to observe, but if you do not have a system of measurement in place, you cannot observe your hypothesis properly. Here’s an example: if you’re experimenting on the effect of healthy food on overall happiness, but you don’t have a way to monitor and measure what “overall happiness” means, your results will not reflect the truth. Monitoring how often someone smiles for a whole day is not reasonably observable, but having the participants state how happy they feel on a scale of one to ten is more observable. 

In writing your hypothesis, always keep in mind how you'll execute the experiment.

#4: Generalizability 

Perhaps you’d like to study what color your best friend wears the most often by observing and documenting the colors she wears each day of the week. This might be fun information for her and you to know, but beyond you two, there aren’t many people who could benefit from this experiment. When you start an experiment, you should note how generalizable your findings may be if they are confirmed. Generalizability is basically how common a particular phenomenon is to other people’s everyday life.

Let’s say you’re asking a question about the health benefits of eating an apple for one day only, you need to realize that the experiment may be too specific to be helpful. It does not help to explain a phenomenon that many people experience. If you find yourself with too specific of a hypothesis, go back to asking the big question: what is it that you want to know, and what do you think will happen between your two variables?

Hypothesis Testing Examples

We know it can be hard to write a good hypothesis unless you’ve seen some good hypothesis examples. We’ve included four hypothesis examples based on some made-up experiments. Use these as templates or launch pads for coming up with your own hypotheses.

Experiment #1: Students Studying Outside (Writing a Hypothesis)

You are a student at PrepScholar University. When you walk around campus, you notice that, when the temperature is above 60 degrees, more students study in the quad. You want to know when your fellow students are more likely to study outside. With this information, how do you make the best hypothesis possible?

You must remember to make additional observations and do secondary research before writing your hypothesis. In doing so, you notice that no one studies outside when it’s 75 degrees and raining, so this should be included in your experiment. Also, studies done on the topic beforehand suggested that students are more likely to study in temperatures less than 85 degrees. With this in mind, you feel confident that you can identify your variables and write your hypotheses:

If-then: “If the temperature in Fahrenheit is less than 60 degrees, significantly fewer students will study outside.”

Null: “If the temperature in Fahrenheit is less than 60 degrees, the same number of students will study outside as when it is more than 60 degrees.”

These hypotheses are plausible, as the temperatures are reasonably within the bounds of what is possible. The number of people in the quad is also easily observable. It is also not a phenomenon specific to only one person or at one time, but instead can explain a phenomenon for a broader group of people.

To complete this experiment, you pick the month of October to observe the quad. Every day (except on the days where it’s raining)from 3 to 4 PM, when most classes have released for the day, you observe how many people are on the quad. You measure how many people come  and how many leave. You also write down the temperature on the hour. 

After writing down all of your observations and putting them on a graph, you find that the most students study on the quad when it is 70 degrees outside, and that the number of students drops a lot once the temperature reaches 60 degrees or below. In this case, your research report would state that you accept or “failed to reject” your first hypothesis with your findings.

Experiment #2: The Cupcake Store (Forming a Simple Experiment)

Let’s say that you work at a bakery. You specialize in cupcakes, and you make only two colors of frosting: yellow and purple. You want to know what kind of customers are more likely to buy what kind of cupcake, so you set up an experiment. Your independent variable is the customer’s gender, and the dependent variable is the color of the frosting. What is an example of a hypothesis that might answer the question of this study?

Here’s what your hypotheses might look like: 

If-then: “If customers’ gender is female, then they will buy more yellow cupcakes than purple cupcakes.”

Null: “If customers’ gender is female, then they will be just as likely to buy purple cupcakes as yellow cupcakes.”

This is a pretty simple experiment! It passes the test of plausibility (there could easily be a difference), defined concepts (there’s nothing complicated about cupcakes!), observability (both color and gender can be easily observed), and general explanation ( this would potentially help you make better business decisions ).

Experiment #3: Backyard Bird Feeders (Integrating Multiple Variables and Rejecting the If-Then Hypothesis)

While watching your backyard bird feeder, you realized that different birds come on the days when you change the types of seeds. You decide that you want to see more cardinals in your backyard, so you decide to see what type of food they like the best and set up an experiment. 

However, one morning, you notice that, while some cardinals are present, blue jays are eating out of your backyard feeder filled with millet. You decide that, of all of the other birds, you would like to see the blue jays the least. This means you'll have more than one variable in your hypothesis. Your new hypotheses might look like this: 

If-then: “If sunflower seeds are placed in the bird feeders, then more cardinals will come than blue jays. If millet is placed in the bird feeders, then more blue jays will come than cardinals.”

Null: “If either sunflower seeds or millet are placed in the bird, equal numbers of cardinals and blue jays will come.”

Through simple observation, you actually find that cardinals come as often as blue jays when sunflower seeds or millet is in the bird feeder. In this case, you would reject your “if-then” hypothesis and “fail to reject” your null hypothesis . You cannot accept your first hypothesis, because it’s clearly not true. Instead you found that there was actually no relation between your different variables. Consequently, you would need to run more experiments with different variables to see if the new variables impact the results.

Experiment #4: In-Class Survey (Including an Alternative Hypothesis)

You’re about to give a speech in one of your classes about the importance of paying attention. You want to take this opportunity to test a hypothesis you’ve had for a while: 

If-then: If students sit in the first two rows of the classroom, then they will listen better than students who do not.

Null: If students sit in the first two rows of the classroom, then they will not listen better or worse than students who do not.

You give your speech and then ask your teacher if you can hand out a short survey to the class. On the survey, you’ve included questions about some of the topics you talked about. When you get back the results, you’re surprised to see that not only do the students in the first two rows not pay better attention, but they also scored worse than students in other parts of the classroom! Here, both your if-then and your null hypotheses are not representative of your findings. What do you do?

This is when you reject both your if-then and null hypotheses and instead create an alternative hypothesis . This type of hypothesis is used in the rare circumstance that neither of your hypotheses is able to capture your findings . Now you can use what you’ve learned to draft new hypotheses and test again! 

Key Takeaways: Hypothesis Writing

The more comfortable you become with writing hypotheses, the better they will become. The structure of hypotheses is flexible and may need to be changed depending on what topic you are studying. The most important thing to remember is the purpose of your hypothesis and the difference between the if-then and the null . From there, in forming your hypothesis, you should constantly be asking questions, making observations, doing secondary research, and considering your variables. After you have written your hypothesis, be sure to edit it so that it is plausible, clearly defined, observable, and helpful in explaining a general phenomenon.

Writing a hypothesis is something that everyone, from elementary school children competing in a science fair to professional scientists in a lab, needs to know how to do. Hypotheses are vital in experiments and in properly executing the scientific method . When done correctly, hypotheses will set up your studies for success and help you to understand the world a little better, one experiment at a time.

What’s Next?

If you’re studying for the science portion of the ACT, there’s definitely a lot you need to know. We’ve got the tools to help, though! Start by checking out our ultimate study guide for the ACT Science subject test. Once you read through that, be sure to download our recommended ACT Science practice tests , since they’re one of the most foolproof ways to improve your score. (And don’t forget to check out our expert guide book , too.)

If you love science and want to major in a scientific field, you should start preparing in high school . Here are the science classes you should take to set yourself up for success.

If you’re trying to think of science experiments you can do for class (or for a science fair!), here’s a list of 37 awesome science experiments you can do at home

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

Student and Parent Forum

Our new student and parent forum, at ExpertHub.PrepScholar.com , allow you to interact with your peers and the PrepScholar staff. See how other students and parents are navigating high school, college, and the college admissions process. Ask questions; get answers.

Ask a Question Below

Have any questions about this article or other topics? Ask below and we'll reply!

Improve With Our Famous Guides

• For All Students

The 5 Strategies You Must Be Using to Improve 160+ SAT Points

How to Get a Perfect 1600, by a Perfect Scorer

Series: How to Get 800 on Each SAT Section:

Score 800 on SAT Math

Score 800 on SAT Reading

Score 800 on SAT Writing

Series: How to Get to 600 on Each SAT Section:

Score 600 on SAT Math

Score 600 on SAT Reading

Score 600 on SAT Writing

Free Complete Official SAT Practice Tests

What SAT Target Score Should You Be Aiming For?

15 Strategies to Improve Your SAT Essay

The 5 Strategies You Must Be Using to Improve 4+ ACT Points

How to Get a Perfect 36 ACT, by a Perfect Scorer

Series: How to Get 36 on Each ACT Section:

36 on ACT English

36 on ACT Math

36 on ACT Reading

36 on ACT Science

Series: How to Get to 24 on Each ACT Section:

24 on ACT English

24 on ACT Math

24 on ACT Reading

24 on ACT Science

What ACT target score should you be aiming for?

ACT Vocabulary You Must Know

ACT Writing: 15 Tips to Raise Your Essay Score

How to Get Into Harvard and the Ivy League

How to Get a Perfect 4.0 GPA

How to Write an Amazing College Essay

What Exactly Are Colleges Looking For?

Is the ACT easier than the SAT? A Comprehensive Guide

Should you retake your SAT or ACT?

When should you take the SAT or ACT?

Stay Informed

Get the latest articles and test prep tips!

Looking for Graduate School Test Prep?

Check out our top-rated graduate blogs here:

GRE Online Prep Blog

GMAT Online Prep Blog

TOEFL Online Prep Blog

Holly R. "I am absolutely overjoyed and cannot thank you enough for helping me!”

Our websites may use cookies to personalize and enhance your experience. By continuing without changing your cookie settings, you agree to this collection. For more information, please see our University Websites Privacy Notice .

Neag School of Education

Educational Research Basics by Del Siegle

Null and alternative hypotheses.

Converting research questions to hypothesis is a simple task. Take the questions and make it a positive statement that says a relationship exists (correlation studies) or a difference exists between the groups (experiment study) and you have the alternative hypothesis. Write the statement such that a relationship does not exist or a difference does not exist and you have the null hypothesis. You can reverse the process if you have a hypothesis and wish to write a research question.

When you are comparing two groups, the groups are the independent variable. When you are testing whether something affects something else, the cause is the independent variable. The independent variable is the one you manipulate.

Teachers given higher pay will have more positive attitudes toward children than teachers given lower pay. The first step is to ask yourself “Are there two or more groups being compared?” The answer is “Yes.” What are the groups? Teachers who are given higher pay and teachers who are given lower pay. The independent variable is teacher pay. The dependent variable (the outcome) is attitude towards school.

You could also approach is another way. “Is something causing something else?” The answer is “Yes.”  What is causing what? Teacher pay is causing attitude towards school. Therefore, teacher pay is the independent variable (cause) and attitude towards school is the dependent variable (outcome).

By tradition, we try to disprove (reject) the null hypothesis. We can never prove a null hypothesis, because it is impossible to prove something does not exist. We can disprove something does not exist by finding an example of it. Therefore, in research we try to disprove the null hypothesis. When we do find that a relationship (or difference) exists then we reject the null and accept the alternative. If we do not find that a relationship (or difference) exists, we fail to reject the null hypothesis (and go with it). We never say we accept the null hypothesis because it is never possible to prove something does not exist. That is why we say that we failed to reject the null hypothesis, rather than we accepted it.

Del Siegle, Ph.D. Neag School of Education – University of Connecticut [email protected] www.delsiegle.com

What Is A Research (Scientific) Hypothesis? A plain-language explainer + examples

By:  Derek Jansen (MBA)  | Reviewed By: Dr Eunice Rautenbach | June 2020

If you’re new to the world of research, or it’s your first time writing a dissertation or thesis, you’re probably noticing that the words “research hypothesis” and “scientific hypothesis” are used quite a bit, and you’re wondering what they mean in a research context .

“Hypothesis” is one of those words that people use loosely, thinking they understand what it means. However, it has a very specific meaning within academic research. So, it’s important to understand the exact meaning before you start hypothesizing. 

Research Hypothesis 101

• What is a hypothesis ?
• What is a research hypothesis (scientific hypothesis)?
• Requirements for a research hypothesis
• Definition of a research hypothesis
• The null hypothesis

What is a hypothesis?

Let’s start with the general definition of a hypothesis (not a research hypothesis or scientific hypothesis), according to the Cambridge Dictionary:

Hypothesis: an idea or explanation for something that is based on known facts but has not yet been proved.

In other words, it’s a statement that provides an explanation for why or how something works, based on facts (or some reasonable assumptions), but that has not yet been specifically tested . For example, a hypothesis might look something like this:

Hypothesis: sleep impacts academic performance.

This statement predicts that academic performance will be influenced by the amount and/or quality of sleep a student engages in – sounds reasonable, right? It’s based on reasonable assumptions , underpinned by what we currently know about sleep and health (from the existing literature). So, loosely speaking, we could call it a hypothesis, at least by the dictionary definition.

But that’s not good enough…

Unfortunately, that’s not quite sophisticated enough to describe a research hypothesis (also sometimes called a scientific hypothesis), and it wouldn’t be acceptable in a dissertation, thesis or research paper . In the world of academic research, a statement needs a few more criteria to constitute a true research hypothesis .

What is a research hypothesis?

A research hypothesis (also called a scientific hypothesis) is a statement about the expected outcome of a study (for example, a dissertation or thesis). To constitute a quality hypothesis, the statement needs to have three attributes – specificity , clarity and testability .

Let’s take a look at these more closely.

Need a helping hand?

Hypothesis Essential #1: Specificity & Clarity

A good research hypothesis needs to be extremely clear and articulate about both what’ s being assessed (who or what variables are involved ) and the expected outcome (for example, a difference between groups, a relationship between variables, etc.).

Let’s stick with our sleepy students example and look at how this statement could be more specific and clear.

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.

As you can see, the statement is very specific as it identifies the variables involved (sleep hours and test grades), the parties involved (two groups of students), as well as the predicted relationship type (a positive relationship). There’s no ambiguity or uncertainty about who or what is involved in the statement, and the expected outcome is clear.

Contrast that to the original hypothesis we looked at – “Sleep impacts academic performance” – and you can see the difference. “Sleep” and “academic performance” are both comparatively vague , and there’s no indication of what the expected relationship direction is (more sleep or less sleep). As you can see, specificity and clarity are key.

Hypothesis Essential #2: Testability (Provability)

A statement must be testable to qualify as a research hypothesis. In other words, there needs to be a way to prove (or disprove) the statement. If it’s not testable, it’s not a hypothesis – simple as that.

For example, consider the hypothesis we mentioned earlier:

Hypothesis: Students who sleep at least 8 hours per night will, on average, achieve higher grades in standardised tests than students who sleep less than 8 hours a night.  

We could test this statement by undertaking a quantitative study involving two groups of students, one that gets 8 or more hours of sleep per night for a fixed period, and one that gets less. We could then compare the standardised test results for both groups to see if there’s a statistically significant difference. 

Again, if you compare this to the original hypothesis we looked at – “Sleep impacts academic performance” – you can see that it would be quite difficult to test that statement, primarily because it isn’t specific enough. How much sleep? By who? What type of academic performance?

So, remember the mantra – if you can’t test it, it’s not a hypothesis 🙂

Defining A Research Hypothesis

You’re still with us? Great! Let’s recap and pin down a clear definition of a hypothesis.

A research hypothesis (or scientific hypothesis) is a statement about an expected relationship between variables, or explanation of an occurrence, that is clear, specific and testable.

So, when you write up hypotheses for your dissertation or thesis, make sure that they meet all these criteria. If you do, you’ll not only have rock-solid hypotheses but you’ll also ensure a clear focus for your entire research project.

What about the null hypothesis?

You may have also heard the terms null hypothesis , alternative hypothesis, or H-zero thrown around. At a simple level, the null hypothesis is the counter-proposal to the original hypothesis.

For example, if the hypothesis predicts that there is a relationship between two variables (for example, sleep and academic performance), the null hypothesis would predict that there is no relationship between those variables.

At a more technical level, the null hypothesis proposes that no statistical significance exists in a set of given observations and that any differences are due to chance alone.

And there you have it – hypotheses in a nutshell. 

If you have any questions, be sure to leave a comment below and we’ll do our best to help you. If you need hands-on help developing and testing your hypotheses, consider our private coaching service , where we hold your hand through the research journey.

Psst… there’s more (for free)

This post is part of our dissertation mini-course, which covers everything you need to get started with your dissertation, thesis or research project. 

You Might Also Like:

16 Comments

Very useful information. I benefit more from getting more information in this regard.

Very great insight,educative and informative. Please give meet deep critics on many research data of public international Law like human rights, environment, natural resources, law of the sea etc

In a book I read a distinction is made between null, research, and alternative hypothesis. As far as I understand, alternative and research hypotheses are the same. Can you please elaborate? Best Afshin

This is a self explanatory, easy going site. I will recommend this to my friends and colleagues.

Very good definition. How can I cite your definition in my thesis? Thank you. Is nul hypothesis compulsory in a research?

It’s a counter-proposal to be proven as a rejection

Please what is the difference between alternate hypothesis and research hypothesis?

It is a very good explanation. However, it limits hypotheses to statistically tasteable ideas. What about for qualitative researches or other researches that involve quantitative data that don’t need statistical tests?

In qualitative research, one typically uses propositions, not hypotheses.

could you please elaborate it more

I’ve benefited greatly from these notes, thank you.

This is very helpful

well articulated ideas are presented here, thank you for being reliable sources of information

Excellent. Thanks for being clear and sound about the research methodology and hypothesis (quantitative research)

I have only a simple question regarding the null hypothesis. – Is the null hypothesis (Ho) known as the reversible hypothesis of the alternative hypothesis (H1? – How to test it in academic research?

this is very important note help me much more

Trackbacks/Pingbacks

• What Is Research Methodology? Simple Definition (With Examples) - Grad Coach - […] Contrasted to this, a quantitative methodology is typically used when the research aims and objectives are confirmatory in nature. For example,…

Submit a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Print Friendly

Introducing Hypothesis for Education

By jeremydean | 26 May, 2015

We have all seized the white perimeter as our own and reached for a pen if only to show we did not just laze in an armchair turning pages; we pressed a thought into the wayside, planted an impression along the verge.

I’ve always been a compulsive annotator, beginning in middle school when I diligently copied my teacher’s comments in class discussion of texts under study into their margins. These were the “modest” notes of the student that Billy Collins writes of in his wonderful ode to “Marginalia.” By the time I went to graduate school, after several years as an English teacher myself, I had developed a more sophisticated system of annotation (special markings for important passages, key terms, etc.) and a distinctive form of underlining.

As a teacher, I always urged my students to write in their books, something they were often resistant to–the value of the trade-in I suppose being contingent on the cleanliness of the copy. I would hand out Collins’ poem in classes at the beginning of every term to at once put my students at ease about annotation–it can just be a “HA!” in the margin as he notes–and to inspire them to read actively and critically, to imagine themselves in conversation with the author.

Collins correctly asserts that annotation is an age-old learning practice, older than books themselves, one used by medieval scribes in the very process of transcription. Traditional annotation aids in both comprehension and analysis for students, it slows the reader down, deepens their engagement. When I write essays, I have my books splayed on my real life desktop, open to passages and lines I’ve marked and am now composing a more close reading around.

I first discovered the power of collaborative annotation when Diigo was introduced at a meeting of the Digital Writing and Research Lab , of which I was a member during my graduate studies at UT-Austin. As a paper kind of guy, I couldn’t see myself using many of the innovative technological tools introduced to us in the DWRL–like teaching composition using Second Life–but collaborative annotation made a certain kind of sense: a simple extension of class discussion, where I urged my students to ground their arguments in textual evidence, as homework. Diigo was clunky but it nonetheless transformed our readings from objects of study into spaces to inhabit. Conversations that started there fed our face-to-face conversations and in turn continued online.

And so several years later when I was procrastinating on Rap Genius instead of working on the final chapter of my dissertation, it wasn’t much of a leap to realize that the platform could be a dynamic teaching tool for the humanities. I ended up adding many of the poems, stories, essays, and even novels I was teaching, and requiring my student to login to Rap Genius multiple times a week and annotate their reading for homework. My use of  Rap Genius in the classroom built on my experience with Diigo, adding a powerful multimedia dimension to annotation-easy and elegant use of images and videos–and making the entire process far more social in the way we’ve come to expect the Internet to be–students upvoting and replying to each other’s annotations, notifications for all such activity that brought them back to the text. Among other texts, my students and I added selections from The Great Gatsby to the platform and some of those excerpts are among the most highly trafficked pages on what has now become Lit Genius , Rap Genius’s literary channel– Chapter I , now it its entirety on the site, has over 650K views.

https://www.youtube.com/watch?v=zIe-ctqVMrM

When Rap Genius received their Series A round of fundraising–$15 million from Andreessen Horowitz–they offered me a job to scale my experiment and build an education department at the company. By the time I left, two and a half years later, we had a vibrant intellectual community of teachers using the site in their classes and regularly collaborating with each other in our Educator forum on how to teach this emergent literacy skill of collaborative annotation. The Education Genius community was a diverse set of educators from around the world, teaching a wide variety of age groups and fields, from high school history students to undergrads in biology ,  to grad students in literary theory .

I’m really proud to have been part of a website that introduced an “Annotate” button to millions of music fans, laying the groundwork for annotation to become an everyday activity for Internet users more broadly. It was an amazing experience to have helped Rap Genius transition to Genius and expand its interactive archive to include a wide range of texts beyond music lyrics. But my vision for collaborative annotation is specifically within formal education. To realize that vision requires focusing resources on the classroom use case in particular and that ultimately wasn’t part of Genius’s priorities. Thinking about education is not just a question of engineering features for the classroom, but also being thoughtful about the politics of platforms. Educators are increasingly more attentive to what kinds of sites and services they are asking their students to sign up for: what will be done with their students’ personal information, and what will be done with the content that their students create? It seemed unlikely to me that Genius would be able to monetize (and thus pay off their investors) without appropriating and commercializing either user data or user content. If we’ve learned anything from Google (and especially Siva Vaidhyanathan’s reading of the company’s phenomenon in The Googlization of Everything ), anything calling itself a knowledge project on the Internet needs to  consider “standards, ensuring the quality and preservation of information worldwide” and be relatively free of the market forces that can compromise the integrity of Internet knowledge production (205).

As a mission-driven organization dedicated to open standards, I think we are poised at Hypothesis to bring annotation to scale in the education space. The school teacher in me remains most focused on classroom applications for this kind of technology, whether that be establishing collaborative digital annotation as a key tool for the implementation of the Common Core Standards in US public schools (see the standards here, annotated and aligned with Hypothesis ), or integrating social reading into online and hybrid learning environments as both a close reading and a community building tool (in fact, thanks to Jesse Stommel, we already had a MOOC on Shakespeare experiment with Hypothesis ). But I also believe that annotation functionality is key to updating our textbooks for the 21st century, making them rich with multimedia elements and editorial notes, but also with the potential for teacher and peer commentary. And I’ll be working to ship annotation along with the Content and Learning Management Systems (C/LMSs) used by so many teachers today as well. With both textbooks and C/LMSs. my vision is to bring the intimacy and vibrancy of a good classroom environment to the digital technologies that supplement IRL teaching moments asynchronously.

If anyone here is interested in the educational uses of annotation technology, please reach out to me. Here are some tutorials  that I’ve created for students and teachers on how to get started using the application. Right now, I’m talking to a lot of former colleagues and current contacts in education about what they think are the most important features of a social reading tool for the classroom. Currently my top three product priorities are: private groups, enhanced notifications, and profile pages. What are yours? I want to know what you and your students need! Reach out anytime for support or discussion: [email protected]. And follow me on Twitter  for live updates and random thoughts about collaborative digital annotation!

Share this article

• Science Notes Posts
• Contact Science Notes
• Todd Helmenstine Biography
• Anne Helmenstine Biography
• Free Printable Periodic Tables (PDF and PNG)
• Periodic Table Wallpapers
• Interactive Periodic Table
• Periodic Table Posters
• How to Grow Crystals
• Chemistry Projects
• Fire and Flames Projects
• Holiday Science
• Chemistry Problems With Answers
• Physics Problems
• Unit Conversion Example Problems
• Chemistry Worksheets
• Biology Worksheets
• Periodic Table Worksheets
• Physical Science Worksheets
• Science Lab Worksheets
• My Amazon Books

Hypothesis Examples

A hypothesis is a prediction of the outcome of a test. It forms the basis for designing an experiment in the scientific method . A good hypothesis is testable, meaning it makes a prediction you can check with observation or experimentation. Here are different hypothesis examples.

Null Hypothesis Examples

The null hypothesis (H 0 ) is also known as the zero-difference or no-difference hypothesis. It predicts that changing one variable ( independent variable ) will have no effect on the variable being measured ( dependent variable ). Here are null hypothesis examples:

• Plant growth is unaffected by temperature.
• If you increase temperature, then solubility of salt will increase.
• Incidence of skin cancer is unrelated to ultraviolet light exposure.
• All brands of light bulb last equally long.
• Cats have no preference for the color of cat food.
• All daisies have the same number of petals.

Sometimes the null hypothesis shows there is a suspected correlation between two variables. For example, if you think plant growth is affected by temperature, you state the null hypothesis: “Plant growth is not affected by temperature.” Why do you do this, rather than say “If you change temperature, plant growth will be affected”? The answer is because it’s easier applying a statistical test that shows, with a high level of confidence, a null hypothesis is correct or incorrect.

Research Hypothesis Examples

A research hypothesis (H 1 ) is a type of hypothesis used to design an experiment. This type of hypothesis is often written as an if-then statement because it’s easy identifying the independent and dependent variables and seeing how one affects the other. If-then statements explore cause and effect. In other cases, the hypothesis shows a correlation between two variables. Here are some research hypothesis examples:

• If you leave the lights on, then it takes longer for people to fall asleep.
• If you refrigerate apples, they last longer before going bad.
• If you keep the curtains closed, then you need less electricity to heat or cool the house (the electric bill is lower).
• If you leave a bucket of water uncovered, then it evaporates more quickly.
• Goldfish lose their color if they are not exposed to light.
• Workers who take vacations are more productive than those who never take time off.

Is It Okay to Disprove a Hypothesis?

Yes! You may even choose to write your hypothesis in such a way that it can be disproved because it’s easier to prove a statement is wrong than to prove it is right. In other cases, if your prediction is incorrect, that doesn’t mean the science is bad. Revising a hypothesis is common. It demonstrates you learned something you did not know before you conducted the experiment.

Test yourself with a Scientific Method Quiz .

• Mellenbergh, G.J. (2008). Chapter 8: Research designs: Testing of research hypotheses. In H.J. Adèr & G.J. Mellenbergh (eds.), Advising on Research Methods: A Consultant’s Companion . Huizen, The Netherlands: Johannes van Kessel Publishing.
• Popper, Karl R. (1959). The Logic of Scientific Discovery . Hutchinson & Co. ISBN 3-1614-8410-X.
• Schick, Theodore; Vaughn, Lewis (2002). How to think about weird things: critical thinking for a New Age . Boston: McGraw-Hill Higher Education. ISBN 0-7674-2048-9.
• Tobi, Hilde; Kampen, Jarl K. (2018). “Research design: the methodology for interdisciplinary research framework”. Quality & Quantity . 52 (3): 1209–1225. doi: 10.1007/s11135-017-0513-8

Null and Alternative Hypotheses

Null hypothesis (h0).

Our teacher support pack has everything students and teachers need to get top marks in the IA. Download a Free preview from https://store.themantic-education.com/

The term “null” means having no value, significance or effect. It also refers to something associated with zero. A null hypothesis in a student’s IA, therefore, should state that there is (or will be) no effect of the IV on the DV. This is what we assume to be true until we have the evidence to suggest otherwise.

A common misconception is that the hypothesis is based on the sample in the study. Our hypotheses should actually be about the population from which we’ve drawn the sample, not the sample itself. Therefore, when writing our hypotheses we can use present tense instead of future tense (e.g. There is instead of There will be… ).

Having said that, in the IB Psych’ IA, the IB is apparently assuming the hypotheses are based on the sample (because variables need to be operationalized) so writing your hypotheses as predictions of what might happen in the experiment is fine (see below for examples).

IB Psych IA Tip: It’s fine (and even recommended) to state in your null hypotheses that there will be no significant difference between the two conditions in your experiment or any differences are due to chance (see footnote 1)

The Alternative Hypothesis (H1)

This is also referred to as the research hypothesis or the experimental hypothesis. It’s an alternative hypothesis to the null because if the null is not true, there must be an alternative explanation.

Generally speaking it’s not a prediction of what will happen in the study, but it’s an assumption about what is true for the population being studied. But, similar to the null hypothesis in the IB Psych IA you can (and should) write this about a prediction of what you think will happen in your study (see examples below).

This must be operationalized: it must be evident how the variables will be quantified, and may be either one- or two-tailed (directional or non-directional).

Read more: 

Operational Definitions

• Key Studies for the IA
• Lesson Idea: Inferential Statistics

To avoid issues with copying and plagiarism, the following examples are from studies that students cannot do for the internal assessment. Some are taken from this post on how to operationalize definitions of variables .

A Fictional Drug Trial

• H1: Taking Paroxetine  will decrease symptoms of PTSD.
• Ho: Taking paroxetine will not decrease symptoms of PTSD.

Operationalized (as if for an IB Psych IA):

• H1: The experimental group who take 20mg of Paroxetine (as a pill) every morning for 7 days will have a larger decrease in symptoms (as measured by the CAPs scale) when compared to the control group who will take an identical placebo pill every morning for 7 days.

A Fictional Study on Body Image*

• H1: Viewing media that portrays the thin ideal increases feelings of body image dissatisfaction.
• Ho: Types of media viewed does not affect body image dissatisfaction.
• H1: Watching a video portraying the thin ideal in a  Baywatch  film trailer will result in higher scores on the Body Shape Questionnaire (BSQ-34) compared with watching media with “normal” body types in the Grownups film trailer.

*This entire IA exemplar is included in the IA Teacher Support Pack.  

A fictional study on weight training.

• H1: Listening to music affects training performance.
• Ho: Music has no effect on training performance.
• H1:  Listening to heavy metal rock music (AC/DC songs) causes a difference in the number of push-ups performed compared to listening to classical music (Mozart’s symphony #41).

One vs. Two Tailed

It is important to know if your hypothesis is one or two-tailed. This will influence the type of inferential statistics test you use later. If you have a one-tailed hypotheses, you should use a one-tailed test. And if you have a two-tailed hypothesis? You guessed it – a two-tailed test.

The one vs two tailed debate still continues in Psychology ( read more ). The IB ignores this and makes it simple: one tailed hypotheses = one tailed test. No ifs, ands, or buts!

If you are predicting that one of your conditions in your experiment will have a higher value than the other, it’s one-tailed (because you know the direction of the effect – the IV is increasing the DV). Similarly, your hypothesis is one-tailed if you are predicting that manipulating the IV will cause a decrease in the DV.

However, if you think your IV will have an effect, but you’re not sure if it will increase  or  decrease it, this is two-tailed.

Of the three examples above, can you tell which one is two-tailed and which one is one-tailed?

Read more about operationally defining your variables in your hypotheses in this blog post .

Points to Remember

• Hypotheses are based on the population, not the sample, so you can write in present tense. However, the norm for IB Psych IA’s is to write in the future tense as a prediction of what will happen in your experiment.
• In IB IA’s, we’re hypothesizing about a causal relationship of an IV on a DV in a population – the hypotheses should reflect that causal relationship.
• Inferential tests are test of the null hypothesis (hence it’s called null hypothesis testing). We are conducting the tests to see the chances of obtaining our results even if the null is true (i.e. there is no effect).

Footnote 1: Saying “that there will be no significant difference between the two conditions in or any differences are due to chance” is technically an incorrect way to state a null hypothesis. That’s because when we conduct our inferential tests we’re seeing what the probability is of getting our results even if our null were true. So if we get a p value of say 0.10 (10%), according to the above null hypothesis we’re saying there is a 10% chance that there will be no significant difference between the two conditions, which isn’t actually accurate (don’t worry if I’ve lost you – it’s mind bending stuff). This is one of those instances where poor statistical practice has ingrained itself in IB assessment. But on the plus side it does make it easier for students (and not enough time is spent on this for the bad habits to be too ingrained anyway).

Travis Dixon is an IB Psychology teacher, author, workshop leader, examiner and IA moderator.

How to Develop a Good Research Hypothesis

The story of a research study begins by asking a question. Researchers all around the globe are asking curious questions and formulating research hypothesis. However, whether the research study provides an effective conclusion depends on how well one develops a good research hypothesis. Research hypothesis examples could help researchers get an idea as to how to write a good research hypothesis.

This blog will help you understand what is a research hypothesis, its characteristics and, how to formulate a research hypothesis

Table of Contents

What is Hypothesis?

Hypothesis is an assumption or an idea proposed for the sake of argument so that it can be tested. It is a precise, testable statement of what the researchers predict will be outcome of the study.  Hypothesis usually involves proposing a relationship between two variables: the independent variable (what the researchers change) and the dependent variable (what the research measures).

What is a Research Hypothesis?

Research hypothesis is a statement that introduces a research question and proposes an expected result. It is an integral part of the scientific method that forms the basis of scientific experiments. Therefore, you need to be careful and thorough when building your research hypothesis. A minor flaw in the construction of your hypothesis could have an adverse effect on your experiment. In research, there is a convention that the hypothesis is written in two forms, the null hypothesis, and the alternative hypothesis (called the experimental hypothesis when the method of investigation is an experiment).

Characteristics of a Good Research Hypothesis

As the hypothesis is specific, there is a testable prediction about what you expect to happen in a study. You may consider drawing hypothesis from previously published research based on the theory.

A good research hypothesis involves more effort than just a guess. In particular, your hypothesis may begin with a question that could be further explored through background research.

To help you formulate a promising research hypothesis, you should ask yourself the following questions:

• Is the language clear and focused?
• What is the relationship between your hypothesis and your research topic?
• Is your hypothesis testable? If yes, then how?
• What are the possible explanations that you might want to explore?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate your variables without hampering the ethical standards?
• Does your research predict the relationship and outcome?
• Is your research simple and concise (avoids wordiness)?
• Is it clear with no ambiguity or assumptions about the readers’ knowledge
• Is your research observable and testable results?
• Is it relevant and specific to the research question or problem?

The questions listed above can be used as a checklist to make sure your hypothesis is based on a solid foundation. Furthermore, it can help you identify weaknesses in your hypothesis and revise it if necessary.

Source: Educational Hub

How to formulate a research hypothesis.

A testable hypothesis is not a simple statement. It is rather an intricate statement that needs to offer a clear introduction to a scientific experiment, its intentions, and the possible outcomes. However, there are some important things to consider when building a compelling hypothesis.

1. State the problem that you are trying to solve.

Make sure that the hypothesis clearly defines the topic and the focus of the experiment.

2. Try to write the hypothesis as an if-then statement.

Follow this template: If a specific action is taken, then a certain outcome is expected.

3. Define the variables

Independent variables are the ones that are manipulated, controlled, or changed. Independent variables are isolated from other factors of the study.

Dependent variables , as the name suggests are dependent on other factors of the study. They are influenced by the change in independent variable.

4. Scrutinize the hypothesis

Evaluate assumptions, predictions, and evidence rigorously to refine your understanding.

Types of Research Hypothesis

The types of research hypothesis are stated below:

1. Simple Hypothesis

It predicts the relationship between a single dependent variable and a single independent variable.

2. Complex Hypothesis

It predicts the relationship between two or more independent and dependent variables.

3. Directional Hypothesis

It specifies the expected direction to be followed to determine the relationship between variables and is derived from theory. Furthermore, it implies the researcher’s intellectual commitment to a particular outcome.

4. Non-directional Hypothesis

It does not predict the exact direction or nature of the relationship between the two variables. The non-directional hypothesis is used when there is no theory involved or when findings contradict previous research.

5. Associative and Causal Hypothesis

The associative hypothesis defines interdependency between variables. A change in one variable results in the change of the other variable. On the other hand, the causal hypothesis proposes an effect on the dependent due to manipulation of the independent variable.

6. Null Hypothesis

Null hypothesis states a negative statement to support the researcher’s findings that there is no relationship between two variables. There will be no changes in the dependent variable due the manipulation of the independent variable. Furthermore, it states results are due to chance and are not significant in terms of supporting the idea being investigated.

7. Alternative Hypothesis

It states that there is a relationship between the two variables of the study and that the results are significant to the research topic. An experimental hypothesis predicts what changes will take place in the dependent variable when the independent variable is manipulated. Also, it states that the results are not due to chance and that they are significant in terms of supporting the theory being investigated.

Research Hypothesis Examples of Independent and Dependent Variables

Research Hypothesis Example 1 The greater number of coal plants in a region (independent variable) increases water pollution (dependent variable). If you change the independent variable (building more coal factories), it will change the dependent variable (amount of water pollution).

Research Hypothesis Example 2 What is the effect of diet or regular soda (independent variable) on blood sugar levels (dependent variable)? If you change the independent variable (the type of soda you consume), it will change the dependent variable (blood sugar levels)

You should not ignore the importance of the above steps. The validity of your experiment and its results rely on a robust testable hypothesis. Developing a strong testable hypothesis has few advantages, it compels us to think intensely and specifically about the outcomes of a study. Consequently, it enables us to understand the implication of the question and the different variables involved in the study. Furthermore, it helps us to make precise predictions based on prior research. Hence, forming a hypothesis would be of great value to the research. Here are some good examples of testable hypotheses.

More importantly, you need to build a robust testable research hypothesis for your scientific experiments. A testable hypothesis is a hypothesis that can be proved or disproved as a result of experimentation.

Importance of a Testable Hypothesis

To devise and perform an experiment using scientific method, you need to make sure that your hypothesis is testable. To be considered testable, some essential criteria must be met:

• There must be a possibility to prove that the hypothesis is true.
• There must be a possibility to prove that the hypothesis is false.
• The results of the hypothesis must be reproducible.

Without these criteria, the hypothesis and the results will be vague. As a result, the experiment will not prove or disprove anything significant.

What are your experiences with building hypotheses for scientific experiments? What challenges did you face? How did you overcome these challenges? Please share your thoughts with us in the comments section.

Frequently Asked Questions

The steps to write a research hypothesis are: 1. Stating the problem: Ensure that the hypothesis defines the research problem 2. Writing a hypothesis as an 'if-then' statement: Include the action and the expected outcome of your study by following a ‘if-then’ structure. 3. Defining the variables: Define the variables as Dependent or Independent based on their dependency to other factors. 4. Scrutinizing the hypothesis: Identify the type of your hypothesis

Hypothesis testing is a statistical tool which is used to make inferences about a population data to draw conclusions for a particular hypothesis.

Hypothesis in statistics is a formal statement about the nature of a population within a structured framework of a statistical model. It is used to test an existing hypothesis by studying a population.

Research hypothesis is a statement that introduces a research question and proposes an expected result. It forms the basis of scientific experiments.

The different types of hypothesis in research are: • Null hypothesis: Null hypothesis is a negative statement to support the researcher’s findings that there is no relationship between two variables. • Alternate hypothesis: Alternate hypothesis predicts the relationship between the two variables of the study. • Directional hypothesis: Directional hypothesis specifies the expected direction to be followed to determine the relationship between variables. • Non-directional hypothesis: Non-directional hypothesis does not predict the exact direction or nature of the relationship between the two variables. • Simple hypothesis: Simple hypothesis predicts the relationship between a single dependent variable and a single independent variable. • Complex hypothesis: Complex hypothesis predicts the relationship between two or more independent and dependent variables. • Associative and casual hypothesis: Associative and casual hypothesis predicts the relationship between two or more independent and dependent variables. • Empirical hypothesis: Empirical hypothesis can be tested via experiments and observation. • Statistical hypothesis: A statistical hypothesis utilizes statistical models to draw conclusions about broader populations.

Wow! You really simplified your explanation that even dummies would find it easy to comprehend. Thank you so much.

Thanks a lot for your valuable guidance.

I enjoy reading the post. Hypotheses are actually an intrinsic part in a study. It bridges the research question and the methodology of the study.

Useful piece!

This is awesome.Wow.

It very interesting to read the topic, can you guide me any specific example of hypothesis process establish throw the Demand and supply of the specific product in market

Nicely explained

It is really a useful for me Kindly give some examples of hypothesis

It was a well explained content ,can you please give me an example with the null and alternative hypothesis illustrated

clear and concise. thanks.

So Good so Amazing

Good to learn

Thanks a lot for explaining to my level of understanding

Explained well and in simple terms. Quick read! Thank you

It awesome. It has really positioned me in my research project

Rate this article Cancel Reply

Your email address will not be published.

Enago Academy's Most Popular Articles

• Reporting Research

Choosing the Right Analytical Approach: Thematic analysis vs. content analysis for data interpretation

In research, choosing the right approach to understand data is crucial for deriving meaningful insights.…

Comparing Cross Sectional and Longitudinal Studies: 5 steps for choosing the right approach

The process of choosing the right research design can put ourselves at the crossroads of…

• Industry News

COPE Forum Discussion Highlights Challenges and Urges Clarity in Institutional Authorship Standards

The COPE forum discussion held in December 2023 initiated with a fundamental question — is…

• Career Corner

Unlocking the Power of Networking in Academic Conferences

Embarking on your first academic conference experience? Fear not, we got you covered! Academic conferences…

Research Recommendations – Guiding policy-makers for evidence-based decision making

Research recommendations play a crucial role in guiding scholars and researchers toward fruitful avenues of…

Choosing the Right Analytical Approach: Thematic analysis vs. content analysis for…

Comparing Cross Sectional and Longitudinal Studies: 5 steps for choosing the right…

How to Design Effective Research Questionnaires for Robust Findings

Sign-up to read more

Subscribe for free to get unrestricted access to all our resources on research writing and academic publishing including:

• 2000+ blog articles
• 50+ Webinars
• 10+ Expert podcasts
• 50+ Infographics
• 10+ Checklists
• Research Guides

We hate spam too. We promise to protect your privacy and never spam you.

I am looking for Editing/ Proofreading services for my manuscript Tentative date of next journal submission:

What should universities' stance be on AI tools in research and academic writing?

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base

Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

Prevent plagiarism. Run a free check.

For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

Bevans, R. (2023, June 22). Hypothesis Testing | A Step-by-Step Guide with Easy Examples. Scribbr. Retrieved April 15, 2024, from https://www.scribbr.com/statistics/hypothesis-testing/

Is this article helpful?

Rebecca Bevans

Other students also liked, choosing the right statistical test | types & examples, understanding p values | definition and examples, what is your plagiarism score.

What Are Examples of a Hypothesis?

• Scientific Method
• Chemical Laws
• Periodic Table
• Projects & Experiments
• Biochemistry
• Physical Chemistry
• Medical Chemistry
• Chemistry In Everyday Life
• Famous Chemists
• Activities for Kids
• Abbreviations & Acronyms
• Weather & Climate
• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

A hypothesis is an explanation for a set of observations. Here are examples of a scientific hypothesis.

Although you could state a scientific hypothesis in various ways, most hypotheses are either "If, then" statements or forms of the null hypothesis . The null hypothesis is sometimes called the "no difference" hypothesis. The null hypothesis is good for experimentation because it's simple to disprove. If you disprove a null hypothesis, that is evidence for a relationship between the variables you are examining.

Examples of Null Hypotheses

• Hyperactivity is unrelated to eating sugar.
• All daisies have the same number of petals.
• The number of pets in a household is unrelated to the number of people living in it.
• A person's preference for a shirt is unrelated to its color.

Examples of If, Then Hypotheses

• If you get at least 6 hours of sleep, you will do better on tests than if you get less sleep.
• If you drop a ball, it will fall toward the ground.
• If you drink coffee before going to bed, then it will take longer to fall asleep.
• If you cover a wound with a bandage, then it will heal with less scarring.

Improving a Hypothesis to Make It Testable

You may wish to revise your first hypothesis in order to make it easier to design an experiment to test. For example, let's say you have a bad breakout the morning after eating a lot of greasy food. You may wonder if there is a correlation between eating greasy food and getting pimples. You propose the hypothesis:

Eating greasy food causes pimples.

Next, you need to design an experiment to test this hypothesis. Let's say you decide to eat greasy food every day for a week and record the effect on your face. Then, as a control, you'll avoid greasy food for the next week and see what happens. Now, this is not a good experiment because it does not take into account other factors such as hormone levels, stress, sun exposure, exercise, or any number of other variables that might conceivably affect your skin.

The problem is that you cannot assign cause to your effect . If you eat french fries for a week and suffer a breakout, can you definitely say it was the grease in the food that caused it? Maybe it was the salt. Maybe it was the potato. Maybe it was unrelated to diet. You can't prove your hypothesis. It's much easier to disprove a hypothesis.

So, let's restate the hypothesis to make it easier to evaluate the data:

Getting pimples is unaffected by eating greasy food.

So, if you eat fatty food every day for a week and suffer breakouts and then don't break out the week that you avoid greasy food, you can be pretty sure something is up. Can you disprove the hypothesis? Probably not, since it is so hard to assign cause and effect. However, you can make a strong case that there is some relationship between diet and acne.

If your skin stays clear for the entire test, you may decide to accept your hypothesis . Again, you didn't prove or disprove anything, which is fine

• Null Hypothesis Definition and Examples
• What Is a Hypothesis? (Science)
• What Are the Elements of a Good Hypothesis?
• Understanding Simple vs Controlled Experiments
• What Is a Testable Hypothesis?
• What 'Fail to Reject' Means in a Hypothesis Test
• Null Hypothesis Examples
• How To Design a Science Fair Experiment
• Scientific Method Vocabulary Terms
• Scientific Hypothesis Examples
• Six Steps of the Scientific Method
• An Example of a Hypothesis Test
• Definition of a Hypothesis
• Scientific Method Flow Chart
• Null Hypothesis and Alternative Hypothesis

• Maths Notes Class 12
• NCERT Solutions Class 12
• RD Sharma Solutions Class 12
• Maths Formulas Class 12
• Maths Previous Year Paper Class 12
• Class 12 Syllabus
• Class 12 Revision Notes
• Physics Notes Class 12
• Chemistry Notes Class 12
• Biology Notes Class 12
• Domain and Range of Trigonometric Functions
• Exponential Graph
• Line Integral
• Determinant of 2x2 Matrix
• Integral of Cos x
• Algebra of Matrices
• Random Sampling
• Derivative of Sin 2x
• Integration
• Derivative of Sec Square x
• Derivative Rules
• Derivative of Sec x
• Systematic Random Sampling
• Derivative of Tan Inverse x
• Derivative of Arctan
• Zero Vector
• Triple Integrals
• Local Maxima and Minima in Calculus

Hypothesis is a testable statement that explains what is happening or observed. It proposes the relation between the various participating variables. Hypothesis is also called Theory, Thesis, Guess, Assumption, or Suggestion. Hypothesis creates a structure that guides the search for knowledge.

In this article, we will learn what is hypothesis, its characteristics, types, and examples. We will also learn how hypothesis helps in scientific research.

What is Hypothesis?

A hypothesis is a suggested idea or plan that has little proof, meant to lead to more study. It’s mainly a smart guess or suggested answer to a problem that can be checked through study and trial. In science work, we make guesses called hypotheses to try and figure out what will happen in tests or watching. These are not sure things but rather ideas that can be proved or disproved based on real-life proofs. A good theory is clear and can be tested and found wrong if the proof doesn’t support it.

Hypothesis Meaning

A hypothesis is a proposed statement that is testable and is given for something that happens or observed.

• It is made using what we already know and have seen, and it’s the basis for scientific research.
• A clear guess tells us what we think will happen in an experiment or study.
• It’s a testable clue that can be proven true or wrong with real-life facts and checking it out carefully.
• It usually looks like a “if-then” rule, showing the expected cause and effect relationship between what’s being studied.

Characteristics of Hypothesis

Here are some key characteristics of a hypothesis:

• Testable: An idea (hypothesis) should be made so it can be tested and proven true through doing experiments or watching. It should show a clear connection between things.
• Specific: It needs to be easy and on target, talking about a certain part or connection between things in a study.
• Falsifiable: A good guess should be able to show it’s wrong. This means there must be a chance for proof or seeing something that goes against the guess.
• Logical and Rational: It should be based on things we know now or have seen, giving a reasonable reason that fits with what we already know.
• Predictive: A guess often tells what to expect from an experiment or observation. It gives a guide for what someone might see if the guess is right.
• Concise: It should be short and clear, showing the suggested link or explanation simply without extra confusion.
• Grounded in Research: A guess is usually made from before studies, ideas or watching things. It comes from a deep understanding of what is already known in that area.
• Flexible: A guess helps in the research but it needs to change or fix when new information comes up.
• Relevant: It should be related to the question or problem being studied, helping to direct what the research is about.
• Empirical: Hypotheses come from observations and can be tested using methods based on real-world experiences.

Sources of Hypothesis

Hypotheses can come from different places based on what you’re studying and the kind of research. Here are some common sources from which hypotheses may originate:

• Existing Theories: Often, guesses come from well-known science ideas. These ideas may show connections between things or occurrences that scientists can look into more.
• Observation and Experience: Watching something happen or having personal experiences can lead to guesses. We notice odd things or repeat events in everyday life and experiments. This can make us think of guesses called hypotheses.
• Previous Research: Using old studies or discoveries can help come up with new ideas. Scientists might try to expand or question current findings, making guesses that further study old results.
• Literature Review: Looking at books and research in a subject can help make guesses. Noticing missing parts or mismatches in previous studies might make researchers think up guesses to deal with these spots.
• Problem Statement or Research Question: Often, ideas come from questions or problems in the study. Making clear what needs to be looked into can help create ideas that tackle certain parts of the issue.
• Analogies or Comparisons: Making comparisons between similar things or finding connections from related areas can lead to theories. Understanding from other fields could create new guesses in a different situation.
• Hunches and Speculation: Sometimes, scientists might get a gut feeling or make guesses that help create ideas to test. Though these may not have proof at first, they can be a beginning for looking deeper.
• Technology and Innovations: New technology or tools might make guesses by letting us look at things that were hard to study before.
• Personal Interest and Curiosity: People’s curiosity and personal interests in a topic can help create guesses. Scientists could make guesses based on their own likes or love for a subject.

Types of Hypothesis

Here are some common types of hypotheses:

Simple Hypothesis

Complex hypothesis, directional hypothesis.

• Non-directional Hypothesis

Null Hypothesis (H0)

Alternative hypothesis (h1 or ha), statistical hypothesis, research hypothesis, associative hypothesis, causal hypothesis.

Simple Hypothesis guesses a connection between two things. It says that there is a connection or difference between variables, but it doesn’t tell us which way the relationship goes.

Complex Hypothesis tells us what will happen when more than two things are connected. It looks at how different things interact and may be linked together.

Directional Hypothesis says how one thing is related to another. For example, it guesses that one thing will help or hurt another thing.

Non-Directional Hypothesis

Non-Directional Hypothesis are the one that don’t say how the relationship between things will be. They just say that there is a connection, without telling which way it goes.

Null hypothesis is a statement that says there’s no connection or difference between different things. It implies that any seen impacts are because of luck or random changes in the information.

Alternative Hypothesis is different from the null hypothesis and shows that there’s a big connection or gap between variables. Scientists want to say no to the null hypothesis and choose the alternative one.

Statistical Hypotheis are used in math testing and include making ideas about what groups or bits of them look like. You aim to get information or test certain things using these top-level, common words only.

Research Hypothesis comes from the research question and tells what link is expected between things or factors. It leads the study and chooses where to look more closely.

Associative Hypotheis guesses that there is a link or connection between things without really saying it caused them. It means that when one thing changes, it is connected to another thing changing.

Causal Hypothesis are different from other ideas because they say that one thing causes another. This means there’s a cause and effect relationship between variables involved in the situation. They say that when one thing changes, it directly makes another thing change.

Hypothesis Examples

Following are the examples of hypotheses based on their types:

Simple Hypothesis Example

• Studying more can help you do better on tests.
• Getting more sun makes people have higher amounts of vitamin D.

Complex Hypothesis Example

• How rich you are, how easy it is to get education and healthcare greatly affects the number of years people live.
• A new medicine’s success relies on the amount used, how old a person is who takes it and their genes.

Directional Hypothesis Example

• Drinking more sweet drinks is linked to a higher body weight score.
• Too much stress makes people less productive at work.

Non-directional Hypothesis Example

• Drinking caffeine can affect how well you sleep.
• People often like different kinds of music based on their gender.
• The average test scores of Group A and Group B are not much different.
• There is no connection between using a certain fertilizer and how much it helps crops grow.

Alternative Hypothesis (Ha)

• Patients on Diet A have much different cholesterol levels than those following Diet B.
• Exposure to a certain type of light can change how plants grow compared to normal sunlight.
• The average smarts score of kids in a certain school area is 100.
• The usual time it takes to finish a job using Method A is the same as with Method B.
• Having more kids go to early learning classes helps them do better in school when they get older.
• Using specific ways of talking affects how much customers get involved in marketing activities.
• Regular exercise helps to lower the chances of heart disease.
• Going to school more can help people make more money.
• Playing violent video games makes teens more likely to act aggressively.
• Less clean air directly impacts breathing health in city populations.

Functions of Hypothesis

Hypotheses have many important jobs in the process of scientific research. Here are the key functions of hypotheses:

• Guiding Research: Hypotheses give a clear and exact way for research. They act like guides, showing the predicted connections or results that scientists want to study.
• Formulating Research Questions: Research questions often create guesses. They assist in changing big questions into particular, checkable things. They guide what the study should be focused on.
• Setting Clear Objectives: Hypotheses set the goals of a study by saying what connections between variables should be found. They set the targets that scientists try to reach with their studies.
• Testing Predictions: Theories guess what will happen in experiments or observations. By doing tests in a planned way, scientists can check if what they see matches the guesses made by their ideas.
• Providing Structure: Theories give structure to the study process by arranging thoughts and ideas. They aid scientists in thinking about connections between things and plan experiments to match.
• Focusing Investigations: Hypotheses help scientists focus on certain parts of their study question by clearly saying what they expect links or results to be. This focus makes the study work better.
• Facilitating Communication: Theories help scientists talk to each other effectively. Clearly made guesses help scientists to tell others what they plan, how they will do it and the results expected. This explains things well with colleagues in a wide range of audiences.
• Generating Testable Statements: A good guess can be checked, which means it can be looked at carefully or tested by doing experiments. This feature makes sure that guesses add to the real information used in science knowledge.
• Promoting Objectivity: Guesses give a clear reason for study that helps guide the process while reducing personal bias. They motivate scientists to use facts and data as proofs or disprovals for their proposed answers.
• Driving Scientific Progress: Making, trying out and adjusting ideas is a cycle. Even if a guess is proven right or wrong, the information learned helps to grow knowledge in one specific area.

How Hypothesis help in Scientific Research?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

• Initiating Investigations: Hypotheses are the beginning of science research. They come from watching, knowing what’s already known or asking questions. This makes scientists make certain explanations that need to be checked with tests.
• Formulating Research Questions: Ideas usually come from bigger questions in study. They help scientists make these questions more exact and testable, guiding the study’s main point.
• Setting Clear Objectives: Hypotheses set the goals of a study by stating what we think will happen between different things. They set the goals that scientists want to reach by doing their studies.
• Designing Experiments and Studies: Assumptions help plan experiments and watchful studies. They assist scientists in knowing what factors to measure, the techniques they will use and gather data for a proposed reason.
• Testing Predictions: Ideas guess what will happen in experiments or observations. By checking these guesses carefully, scientists can see if the seen results match up with what was predicted in each hypothesis.
• Analysis and Interpretation of Data: Hypotheses give us a way to study and make sense of information. Researchers look at what they found and see if it matches the guesses made in their theories. They decide if the proof backs up or disagrees with these suggested reasons why things are happening as expected.
• Encouraging Objectivity: Hypotheses help make things fair by making sure scientists use facts and information to either agree or disagree with their suggested reasons. They lessen personal preferences by needing proof from experience.
• Iterative Process: People either agree or disagree with guesses, but they still help the ongoing process of science. Findings from testing ideas make us ask new questions, improve those ideas and do more tests. It keeps going on in the work of science to keep learning things.

People Also View:

Mathematics Maths Formulas Branches of Mathematics

Summary – Hypothesis

A hypothesis is a testable statement serving as an initial explanation for phenomena, based on observations, theories, or existing knowledge. It acts as a guiding light for scientific research, proposing potential relationships between variables that can be empirically tested through experiments and observations. The hypothesis must be specific, testable, falsifiable, and grounded in prior research or observation, laying out a predictive, if-then scenario that details a cause-and-effect relationship. It originates from various sources including existing theories, observations, previous research, and even personal curiosity, leading to different types, such as simple, complex, directional, non-directional, null, and alternative hypotheses, each serving distinct roles in research methodology. The hypothesis not only guides the research process by shaping objectives and designing experiments but also facilitates objective analysis and interpretation of data, ultimately driving scientific progress through a cycle of testing, validation, and refinement.

FAQs on Hypothesis

What is a hypothesis.

A guess is a possible explanation or forecast that can be checked by doing research and experiments.

What are Components of a Hypothesis?

The components of a Hypothesis are Independent Variable, Dependent Variable, Relationship between Variables, Directionality etc.

What makes a Good Hypothesis?

Testability, Falsifiability, Clarity and Precision, Relevance are some parameters that makes a Good Hypothesis

Can a Hypothesis be Proven True?

You cannot prove conclusively that most hypotheses are true because it’s generally impossible to examine all possible cases for exceptions that would disprove them.

How are Hypotheses Tested?

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data

Can Hypotheses change during Research?

Yes, you can change or improve your ideas based on new information discovered during the research process.

What is the Role of a Hypothesis in Scientific Research?

Hypotheses are used to support scientific research and bring about advancements in knowledge.

Please Login to comment...

Similar reads.

• Geeks Premier League 2023
• Maths-Class-12
• Geeks Premier League
• Mathematics
• School Learning
• What are Tiktok AI Avatars?
• Poe Introduces A Price-per-message Revenue Model For AI Bot Creators
• Truecaller For Web Now Available For Android Users In India
• Google Introduces New AI-powered Vids App
• 30 OOPs Interview Questions and Answers (2024)

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons
• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

9.8: Hypothesis Testing with One Sample (Exercises)

• Last updated
• Save as PDF
• Page ID 4944

These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

9.1: Introduction

9.2: null and alternative hypotheses.

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.

State the null hypothesis, \(H_{0}\), and the alternative hypothesis. \(H_{a}\), in terms of the appropriate parameter \((\mu \text{or} p)\).

• The mean number of years Americans work before retiring is 34.
• At most 60% of Americans vote in presidential elections.
• The mean starting salary for San Jose State University graduates is at least $100,000 per year.
• Twenty-nine percent of high school seniors get drunk each month.
• Fewer than 5% of adults ride the bus to work in Los Angeles.
• The mean number of cars a person owns in her lifetime is not more than ten.
• About half of Americans prefer to live away from cities, given the choice.
• Europeans have a mean paid vacation each year of six weeks.
• The chance of developing breast cancer is under 11% for women.
• Private universities' mean tuition cost is more than $20,000 per year.
• \(H_{0}: \mu = 34; H_{a}: \mu \neq 34\)
• \(H_{0}: p \leq 0.60; H_{a}: p > 0.60\)
• \(H_{0}: \mu \geq 100,000; H_{a}: \mu < 100,000\)
• \(H_{0}: p = 0.29; H_{a}: p \neq 0.29\)
• \(H_{0}: p = 0.05; H_{a}: p < 0.05\)
• \(H_{0}: \mu \leq 10; H_{a}: \mu > 10\)
• \(H_{0}: p = 0.50; H_{a}: p \neq 0.50\)
• \(H_{0}: \mu = 6; H_{a}: \mu \neq 6\)
• \(H_{0}: p ≥ 0.11; H_{a}: p < 0.11\)
• \(H_{0}: \mu \leq 20,000; H_{a}: \mu > 20,000\)

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is:

• \(p < 0.30\)
• \(p \leq 0.30\)
• \(p \geq 0.30\)
• \(p > 0.30\)

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:

• \(p = 0.20\)
• \(p > 0.20\)
• \(p < 0.20\)
• \(p \leq 0.20\)

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are:

• \(H_{0}: \bar{x} = 4.5, H_{a}: \bar{x} > 4.5\)
• \(H_{0}: \mu \geq 4.5, H_{a}: \mu < 4.5\)
• \(H_{0}: \mu = 4.75, H_{a}: \mu > 4.75\)
• \(H_{0}: \mu = 4.5, H_{a}: \mu > 4.5\)

9.3: Outcomes and the Type I and Type II Errors

State the Type I and Type II errors in complete sentences given the following statements.

• The mean number of cars a person owns in his or her lifetime is not more than ten.
• Private universities mean tuition cost is more than $20,000 per year.
• Type I error: We conclude that the mean is not 34 years, when it really is 34 years. Type II error: We conclude that the mean is 34 years, when in fact it really is not 34 years.
• Type I error: We conclude that more than 60% of Americans vote in presidential elections, when the actual percentage is at most 60%.Type II error: We conclude that at most 60% of Americans vote in presidential elections when, in fact, more than 60% do.
• Type I error: We conclude that the mean starting salary is less than $100,000, when it really is at least $100,000. Type II error: We conclude that the mean starting salary is at least $100,000 when, in fact, it is less than $100,000.
• Type I error: We conclude that the proportion of high school seniors who get drunk each month is not 29%, when it really is 29%. Type II error: We conclude that the proportion of high school seniors who get drunk each month is 29% when, in fact, it is not 29%.
• Type I error: We conclude that fewer than 5% of adults ride the bus to work in Los Angeles, when the percentage that do is really 5% or more. Type II error: We conclude that 5% or more adults ride the bus to work in Los Angeles when, in fact, fewer that 5% do.
• Type I error: We conclude that the mean number of cars a person owns in his or her lifetime is more than 10, when in reality it is not more than 10. Type II error: We conclude that the mean number of cars a person owns in his or her lifetime is not more than 10 when, in fact, it is more than 10.
• Type I error: We conclude that the proportion of Americans who prefer to live away from cities is not about half, though the actual proportion is about half. Type II error: We conclude that the proportion of Americans who prefer to live away from cities is half when, in fact, it is not half.
• Type I error: We conclude that the duration of paid vacations each year for Europeans is not six weeks, when in fact it is six weeks. Type II error: We conclude that the duration of paid vacations each year for Europeans is six weeks when, in fact, it is not.
• Type I error: We conclude that the proportion is less than 11%, when it is really at least 11%. Type II error: We conclude that the proportion of women who develop breast cancer is at least 11%, when in fact it is less than 11%.
• Type I error: We conclude that the average tuition cost at private universities is more than $20,000, though in reality it is at most $20,000. Type II error: We conclude that the average tuition cost at private universities is at most $20,000 when, in fact, it is more than $20,000.

For statements a-j in Exercise 9.109 , answer the following in complete sentences.

• State a consequence of committing a Type I error.
• State a consequence of committing a Type II error.

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is “the drug is unsafe.” What is the Type II Error?

• To conclude the drug is safe when in, fact, it is unsafe.
• Not to conclude the drug is safe when, in fact, it is safe.
• To conclude the drug is safe when, in fact, it is safe.
• Not to conclude the drug is unsafe when, in fact, it is unsafe.

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of EVC students who attended is ________.

• at least 20%, when in fact, it is less than 20%.
• 20%, when in fact, it is 20%.
• less than 20%, when in fact, it is at least 20%.
• less than 20%, when in fact, it is less than 20%.

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average?

The Type II error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when, in fact, the mean number of hours

• is more than seven hours.
• is at most seven hours.
• is at least seven hours.
• is less than seven hours.

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:

• to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher
• to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same
• to conclude that the mean hours per week currently is 4.5, when in fact, it is higher
• to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

9.4: Distribution Needed for Hypothesis Testing

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average? The distribution to be used for this test is \(\bar{X} \sim\) ________________

• \(N\left(7.24, \frac{1.93}{\sqrt{22}}\right)\)
• \(N\left(7.24, 1.93\right)\)

9.5: Rare Events, the Sample, Decision and Conclusion

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population.

• Is this a test of one mean or proportion?
• State the null and alternative hypotheses. \(H_{0}\) : ____________________ \(H_{a}\) : ____________________
• Is this a right-tailed, left-tailed, or two-tailed test?
• What symbol represents the random variable for this test?
• In words, define the random variable for this test.
• \(x =\) ________________
• \(n =\) ________________
• \(p′ =\) _____________
• Calculate \(\sigma_{x} =\) __________. Show the formula set-up.
• State the distribution to use for the hypothesis test.
• Find the \(p\text{-value}\).
• Reason for the decision:
• Conclusion (write out in a complete sentence):

9.6: Additional Information and Full Hypothesis Test Examples

For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in [link] . Please feel free to make copies of the solution sheets. For the online version of the book, it is suggested that you copy the .doc or the .pdf files.

If you are using a Student's \(t\) - distribution for one of the following homework problems, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, however.)

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using \(\alpha = 0.05\), is the data highly inconsistent with the claim?

• \(H_{0}: \mu \geq 50,000\)
• \(H_{a}: \mu < 50,000\)
• Let \(\bar{X} =\) the average lifespan of a brand of tires.
• normal distribution
• \(z = -2.315\)
• \(p\text{-value} = 0.0103\)
• Check student’s solution.
• alpha: 0.05
• Decision: Reject the null hypothesis.
• Reason for decision: The \(p\text{-value}\) is less than 0.05.
• Conclusion: There is sufficient evidence to conclude that the mean lifespan of the tires is less than 50,000 miles.
• \((43,537, 49,463)\)

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant of around 2.1 years. A survey of 40 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

The cost of a daily newspaper varies from city to city. However, the variation among prices remains steady with a standard deviation of 20¢. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of 95¢ with a standard deviation of 18¢. Do the data support the claim at the 1% level?

• \(H_{0}: \mu = $1.00\)
• \(H_{a}: \mu \neq $1.00\)
• Let \(\bar{X} =\) the average cost of a daily newspaper.
• \(z = –0.866\)
• \(p\text{-value} = 0.3865\)
• \(\alpha: 0.01\)
• Decision: Do not reject the null hypothesis.
• Reason for decision: The \(p\text{-value}\) is greater than 0.01.
• Conclusion: There is sufficient evidence to support the claim that the mean cost of daily papers is $1. The mean cost could be $1.
• \(($0.84, $1.06)\)

An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of 49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?

The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Let \(x =\) the number of sick days they took for the past year. Should the personnel team believe that the mean number is ten?

• \(H_{0}: \mu = 10\)
• \(H_{a}: \mu \neq 10\)
• Let \(\bar{X}\) the mean number of sick days an employee takes per year.
• Student’s t -distribution
• \(t = –1.12\)
• \(p\text{-value} = 0.300\)
• \(\alpha: 0.05\)
• Reason for decision: The \(p\text{-value}\) is greater than 0.05.
• Conclusion: At the 5% significance level, there is insufficient evidence to conclude that the mean number of sick days is not ten.
• \((4.9443, 11.806)\)

In 1955, Life Magazine reported that the 25 year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or not the women's movement has, in fact, resulted in an increase in the average work week for women (combining employment and at-home work). Suppose a study was done to determine if the mean work week has increased. 81 women were surveyed with the following results. The sample mean was 83; the sample standard deviation was ten. Does it appear that the mean work week has increased for women at the 5% level?

Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Now, what do you think?

• \(H_{0}: p \geq 0.6\)
• \(H_{a}: p < 0.6\)
• Let \(P′ =\) the proportion of students who feel more enriched as a result of taking Elementary Statistics.
• normal for a single proportion
• \(p\text{-value} = 0.1308\)
• Conclusion: There is insufficient evidence to conclude that less than 60 percent of her students feel more enriched.

The “plus-4s” confidence interval is \((0.411, 0.648)\)

A Nissan Motor Corporation advertisement read, “The average man’s I.Q. is 107. The average brown trout’s I.Q. is 4. So why can’t man catch brown trout?” Suppose you believe that the brown trout’s mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologist determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief.

Refer to Exercise 9.119 . Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trout’s mean I.Q. is not four.

• \(H_{0}: \mu = 4\)
• \(H_{a}: \mu \neq 4\)
• Let \(\bar{X}\) the average I.Q. of a set of brown trout.
• two-tailed Student's t-test
• \(t = 1.95\)
• \(p\text{-value} = 0.076\)
• Reason for decision: The \(p\text{-value}\) is greater than 0.05
• Conclusion: There is insufficient evidence to conclude that the average IQ of brown trout is not four.
• \((3.8865,5.9468)\)

According to an article in Newsweek , the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don’t believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7?

A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent’s survey, would you agree with the Newsweek poll? In complete sentences, also give three reasons why the two polls might give different results.

• \(H_{a}: p < 0.13\)
• Let \(P′ =\) the proportion of Americans who have seen or sensed angels
• –2.688
• \(p\text{-value} = 0.0036\)
• Reason for decision: The \(p\text{-value}\)e is less than 0.05.
• Conclusion: There is sufficient evidence to conclude that the percentage of Americans who have seen or sensed an angel is less than 13%.

The“plus-4s” confidence interval is (0.0022, 0.0978)

The mean work week for engineers in a start-up company is believed to be about 60 hours. A newly hired engineer hopes that it’s shorter. She asks ten engineering friends in start-ups for the lengths of their mean work weeks. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours?

Data (length of mean work week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.

Use the “Lap time” data for Lap 4 (see [link] ) to test the claim that Terri finishes Lap 4, on average, in less than 129 seconds. Use all twenty races given.

• \(H_{0}: \mu \geq 129\)
• \(H_{a}: \mu < 129\)
• Let \(\bar{X} =\) the average time in seconds that Terri finishes Lap 4.
• Student's t -distribution
• \(t = 1.209\)
• Conclusion: There is insufficient evidence to conclude that Terri’s mean lap time is less than 129 seconds.
• \((128.63, 130.37)\)

Use the “Initial Public Offering” data (see [link] ) to test the claim that the mean offer price was $18 per share. Do not use all the data. Use your random number generator to randomly survey 15 prices.

The following questions were written by past students. They are excellent problems!

"Asian Family Reunion," by Chau Nguyen

Every two years it comes around.

We all get together from different towns.

In my honest opinion,

It's not a typical family reunion.

Not forty, or fifty, or sixty,

But how about seventy companions!

The kids would play, scream, and shout

One minute they're happy, another they'll pout.

The teenagers would look, stare, and compare

From how they look to what they wear.

The men would chat about their business

That they make more, but never less.

Money is always their subject

And there's always talk of more new projects.

The women get tired from all of the chats

They head to the kitchen to set out the mats.

Some would sit and some would stand

Eating and talking with plates in their hands.

Then come the games and the songs

And suddenly, everyone gets along!

With all that laughter, it's sad to say

That it always ends in the same old way.

They hug and kiss and say "good-bye"

And then they all begin to cry!

I say that 60 percent shed their tears

But my mom counted 35 people this year.

She said that boys and men will always have their pride,

So we won't ever see them cry.

I myself don't think she's correct,

So could you please try this problem to see if you object?

• \(H_{0}: p = 0.60\)
• \(H_{a}: p < 0.60\)
• Let \(P′ =\) the proportion of family members who shed tears at a reunion.
• –1.71
• Reason for decision: \(p\text{-value} < \alpha\)
• Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the proportion of family members who shed tears at a reunion is less than 0.60. However, the test is weak because the \(p\text{-value}\) and alpha are quite close, so other tests should be done.
• We are 95% confident that between 38.29% and 61.71% of family members will shed tears at a family reunion. \((0.3829, 0.6171)\). The“plus-4s” confidence interval (see chapter 8) is \((0.3861, 0.6139)\)

Note that here the “large-sample” \(1 - \text{PropZTest}\) provides the approximate \(p\text{-value}\) of 0.0438. Whenever a \(p\text{-value}\) based on a normal approximation is close to the level of significance, the exact \(p\text{-value}\) based on binomial probabilities should be calculated whenever possible. This is beyond the scope of this course.

"The Problem with Angels," by Cyndy Dowling

Although this problem is wholly mine,

The catalyst came from the magazine, Time.

On the magazine cover I did find

The realm of angels tickling my mind.

Inside, 69% I found to be

In angels, Americans do believe.

Then, it was time to rise to the task,

Ninety-five high school and college students I did ask.

Viewing all as one group,

Random sampling to get the scoop.

So, I asked each to be true,

"Do you believe in angels?" Tell me, do!

Hypothesizing at the start,

Totally believing in my heart

That the proportion who said yes

Would be equal on this test.

Lo and behold, seventy-three did arrive,

Out of the sample of ninety-five.

Now your job has just begun,

Solve this problem and have some fun.

"Blowing Bubbles," by Sondra Prull

Studying stats just made me tense,

I had to find some sane defense.

Some light and lifting simple play

To float my math anxiety away.

Blowing bubbles lifts me high

Takes my troubles to the sky.

POIK! They're gone, with all my stress

Bubble therapy is the best.

The label said each time I blew

The average number of bubbles would be at least 22.

I blew and blew and this I found

From 64 blows, they all are round!

But the number of bubbles in 64 blows

Varied widely, this I know.

20 per blow became the mean

They deviated by 6, and not 16.

From counting bubbles, I sure did relax

But now I give to you your task.

Was 22 a reasonable guess?

Find the answer and pass this test!

• \(H_{0}: \mu \geq 22\)
• \(H_{a}: \mu < 22\)
• Let \(\bar{X} =\) the mean number of bubbles per blow.
• –2.667
• \(p\text{-value} = 0.00486\)
• Conclusion: There is sufficient evidence to conclude that the mean number of bubbles per blow is less than 22.
• \((18.501, 21.499)\)

"Dalmatian Darnation," by Kathy Sparling

A greedy dog breeder named Spreckles

Bred puppies with numerous freckles

The Dalmatians he sought

Possessed spot upon spot

The more spots, he thought, the more shekels.

His competitors did not agree

That freckles would increase the fee.

They said, “Spots are quite nice

But they don't affect price;

One should breed for improved pedigree.”

The breeders decided to prove

This strategy was a wrong move.

Breeding only for spots

Would wreak havoc, they thought.

His theory they want to disprove.

They proposed a contest to Spreckles

Comparing dog prices to freckles.

In records they looked up

One hundred one pups:

Dalmatians that fetched the most shekels.

They asked Mr. Spreckles to name

An average spot count he'd claim

To bring in big bucks.

Said Spreckles, “Well, shucks,

It's for one hundred one that I aim.”

Said an amateur statistician

Who wanted to help with this mission.

“Twenty-one for the sample

Standard deviation's ample:

They examined one hundred and one

Dalmatians that fetched a good sum.

They counted each spot,

Mark, freckle and dot

And tallied up every one.

Instead of one hundred one spots

They averaged ninety six dots

Can they muzzle Spreckles’

Obsession with freckles

Based on all the dog data they've got?

"Macaroni and Cheese, please!!" by Nedda Misherghi and Rachelle Hall

As a poor starving student I don't have much money to spend for even the bare necessities. So my favorite and main staple food is macaroni and cheese. It's high in taste and low in cost and nutritional value.

One day, as I sat down to determine the meaning of life, I got a serious craving for this, oh, so important, food of my life. So I went down the street to Greatway to get a box of macaroni and cheese, but it was SO expensive! $2.02 !!! Can you believe it? It made me stop and think. The world is changing fast. I had thought that the mean cost of a box (the normal size, not some super-gigantic-family-value-pack) was at most $1, but now I wasn't so sure. However, I was determined to find out. I went to 53 of the closest grocery stores and surveyed the prices of macaroni and cheese. Here are the data I wrote in my notebook:

Price per box of Mac and Cheese:

• 5 stores @ $2.02
• 15 stores @ $0.25
• 3 stores @ $1.29
• 6 stores @ $0.35
• 4 stores @ $2.27
• 7 stores @ $1.50
• 5 stores @ $1.89
• 8 stores @ 0.75.

I could see that the cost varied but I had to sit down to figure out whether or not I was right. If it does turn out that this mouth-watering dish is at most $1, then I'll throw a big cheesy party in our next statistics lab, with enough macaroni and cheese for just me. (After all, as a poor starving student I can't be expected to feed our class of animals!)

• \(H_{0}: \mu \leq 1\)
• \(H_{a}: \mu > 1\)
• Let \(\bar{X} =\) the mean cost in dollars of macaroni and cheese in a certain town.
• Student's \(t\)-distribution
• \(t = 0.340\)
• \(p\text{-value} = 0.36756\)
• Conclusion: The mean cost could be $1, or less. At the 5% significance level, there is insufficient evidence to conclude that the mean price of a box of macaroni and cheese is more than $1.
• \((0.8291, 1.241)\)

"William Shakespeare: The Tragedy of Hamlet, Prince of Denmark," by Jacqueline Ghodsi

THE CHARACTERS (in order of appearance):

• HAMLET, Prince of Denmark and student of Statistics
• POLONIUS, Hamlet’s tutor
• HOROTIO, friend to Hamlet and fellow student

Scene: The great library of the castle, in which Hamlet does his lessons

(The day is fair, but the face of Hamlet is clouded. He paces the large room. His tutor, Polonius, is reprimanding Hamlet regarding the latter’s recent experience. Horatio is seated at the large table at right stage.)

POLONIUS: My Lord, how cans’t thou admit that thou hast seen a ghost! It is but a figment of your imagination!

HAMLET: I beg to differ; I know of a certainty that five-and-seventy in one hundred of us, condemned to the whips and scorns of time as we are, have gazed upon a spirit of health, or goblin damn’d, be their intents wicked or charitable.

POLONIUS If thou doest insist upon thy wretched vision then let me invest your time; be true to thy work and speak to me through the reason of the null and alternate hypotheses. (He turns to Horatio.) Did not Hamlet himself say, “What piece of work is man, how noble in reason, how infinite in faculties? Then let not this foolishness persist. Go, Horatio, make a survey of three-and-sixty and discover what the true proportion be. For my part, I will never succumb to this fantasy, but deem man to be devoid of all reason should thy proposal of at least five-and-seventy in one hundred hold true.

HORATIO (to Hamlet): What should we do, my Lord?

HAMLET: Go to thy purpose, Horatio.

HORATIO: To what end, my Lord?

HAMLET: That you must teach me. But let me conjure you by the rights of our fellowship, by the consonance of our youth, but the obligation of our ever-preserved love, be even and direct with me, whether I am right or no.

(Horatio exits, followed by Polonius, leaving Hamlet to ponder alone.)

(The next day, Hamlet awaits anxiously the presence of his friend, Horatio. Polonius enters and places some books upon the table just a moment before Horatio enters.)

POLONIUS: So, Horatio, what is it thou didst reveal through thy deliberations?

HORATIO: In a random survey, for which purpose thou thyself sent me forth, I did discover that one-and-forty believe fervently that the spirits of the dead walk with us. Before my God, I might not this believe, without the sensible and true avouch of mine own eyes.

POLONIUS: Give thine own thoughts no tongue, Horatio. (Polonius turns to Hamlet.) But look to’t I charge you, my Lord. Come Horatio, let us go together, for this is not our test. (Horatio and Polonius leave together.)

HAMLET: To reject, or not reject, that is the question: whether ‘tis nobler in the mind to suffer the slings and arrows of outrageous statistics, or to take arms against a sea of data, and, by opposing, end them. (Hamlet resignedly attends to his task.)

(Curtain falls)

"Untitled," by Stephen Chen

I've often wondered how software is released and sold to the public. Ironically, I work for a company that sells products with known problems. Unfortunately, most of the problems are difficult to create, which makes them difficult to fix. I usually use the test program X, which tests the product, to try to create a specific problem. When the test program is run to make an error occur, the likelihood of generating an error is 1%.

So, armed with this knowledge, I wrote a new test program Y that will generate the same error that test program X creates, but more often. To find out if my test program is better than the original, so that I can convince the management that I'm right, I ran my test program to find out how often I can generate the same error. When I ran my test program 50 times, I generated the error twice. While this may not seem much better, I think that I can convince the management to use my test program instead of the original test program. Am I right?

• \(H_{0}: p = 0.01\)
• \(H_{a}: p > 0.01\)
• Let \(P′ =\) the proportion of errors generated
• Normal for a single proportion
• Decision: Reject the null hypothesis
• Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the proportion of errors generated is more than 0.01.

The“plus-4s” confidence interval is \((0.004, 0.144)\).

"Japanese Girls’ Names"

by Kumi Furuichi

It used to be very typical for Japanese girls’ names to end with “ko.” (The trend might have started around my grandmothers’ generation and its peak might have been around my mother’s generation.) “Ko” means “child” in Chinese characters. Parents would name their daughters with “ko” attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachiko—happy child, Yoshiko—a good child, Yasuko—a healthy child, and so on.

However, I noticed recently that only two out of nine of my Japanese girlfriends at this school have names which end with “ko.” More and more, parents seem to have become creative, modernized, and, sometimes, westernized in naming their children.

I have a feeling that, while 70 percent or more of my mother’s generation would have names with “ko” at the end, the proportion has dropped among my peers. I wrote down all my Japanese friends’, ex-classmates’, co-workers, and acquaintances’ names that I could remember. Following are the names. (Some are repeats.) Test to see if the proportion has dropped for this generation.

Ai, Akemi, Akiko, Ayumi, Chiaki, Chie, Eiko, Eri, Eriko, Fumiko, Harumi, Hitomi, Hiroko, Hiroko, Hidemi, Hisako, Hinako, Izumi, Izumi, Junko, Junko, Kana, Kanako, Kanayo, Kayo, Kayoko, Kazumi, Keiko, Keiko, Kei, Kumi, Kumiko, Kyoko, Kyoko, Madoka, Maho, Mai, Maiko, Maki, Miki, Miki, Mikiko, Mina, Minako, Miyako, Momoko, Nana, Naoko, Naoko, Naoko, Noriko, Rieko, Rika, Rika, Rumiko, Rei, Reiko, Reiko, Sachiko, Sachiko, Sachiyo, Saki, Sayaka, Sayoko, Sayuri, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yuki, Yuki, Yukiko, Yuko, Yuko.

"Phillip’s Wish," by Suzanne Osorio

My nephew likes to play

Chasing the girls makes his day.

He asked his mother

If it is okay

To get his ear pierced.

She said, “No way!”

To poke a hole through your ear,

Is not what I want for you, dear.

He argued his point quite well,

Says even my macho pal, Mel,

Has gotten this done.

It’s all just for fun.

C’mon please, mom, please, what the hell.

Again Phillip complained to his mother,

Saying half his friends (including their brothers)

Are piercing their ears

And they have no fears

He wants to be like the others.

She said, “I think it’s much less.

We must do a hypothesis test.

And if you are right,

I won’t put up a fight.

But, if not, then my case will rest.”

We proceeded to call fifty guys

To see whose prediction would fly.

Nineteen of the fifty

Said piercing was nifty

And earrings they’d occasionally buy.

Then there’s the other thirty-one,

Who said they’d never have this done.

So now this poem’s finished.

Will his hopes be diminished,

Or will my nephew have his fun?

• \(H_{0}: p = 0.50\)
• \(H_{a}: p < 0.50\)
• Let \(P′ =\) the proportion of friends that has a pierced ear.
• –1.70
• \(p\text{-value} = 0.0448\)
• Reason for decision: The \(p\text{-value}\) is less than 0.05. (However, they are very close.)
• Conclusion: There is sufficient evidence to support the claim that less than 50% of his friends have pierced ears.
• Confidence Interval: \((0.245, 0.515)\): The “plus-4s” confidence interval is \((0.259, 0.519)\).

"The Craven," by Mark Salangsang

Once upon a morning dreary

In stats class I was weak and weary.

Pondering over last night’s homework

Whose answers were now on the board

This I did and nothing more.

While I nodded nearly napping

Suddenly, there came a tapping.

As someone gently rapping,

Rapping my head as I snore.

Quoth the teacher, “Sleep no more.”

“In every class you fall asleep,”

The teacher said, his voice was deep.

“So a tally I’ve begun to keep

Of every class you nap and snore.

The percentage being forty-four.”

“My dear teacher I must confess,

While sleeping is what I do best.

The percentage, I think, must be less,

A percentage less than forty-four.”

This I said and nothing more.

“We’ll see,” he said and walked away,

And fifty classes from that day

He counted till the month of May

The classes in which I napped and snored.

The number he found was twenty-four.

At a significance level of 0.05,

Please tell me am I still alive?

Or did my grade just take a dive

Plunging down beneath the floor?

Upon thee I hereby implore.

Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

• \(H_{0}: p = 0.40\)
• \(H_{a}: p < 0.40\)
• Let \(P′ =\) the proportion of schoolmates who fear public speaking.
• –1.01
• \(p\text{-value} = 0.1563\)
• Conclusion: There is insufficient evidence to support the claim that less than 40% of students at the school fear public speaking.
• Confidence Interval: \((0.3241, 0.4240)\): The “plus-4s” confidence interval is \((0.3257, 0.4250)\).

Sixty-eight percent of online courses taught at community colleges nationwide were taught by full-time faculty. To test if 68% also represents California’s percent for full-time faculty teaching the online classes, Long Beach City College (LBCC) in California, was randomly selected for comparison. In the same year, 34 of the 44 online courses LBCC offered were taught by full-time faculty. Conduct a hypothesis test to determine if 68% represents California. NOTE: For more accurate results, use more California community colleges and this past year's data.

According to an article in Bloomberg Businessweek , New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year’s rate. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased.

• \(H_{0}: p = 0.14\)
• \(H_{a}: p < 0.14\)
• Let \(P′ =\) the proportion of NYC residents that smoke.
• –0.2756
• \(p\text{-value} = 0.3914\)
• At the 5% significance level, there is insufficient evidence to conclude that the proportion of NYC residents who smoke is less than 0.14.
• Confidence Interval: \((0.0502, 0.2070)\): The “plus-4s” confidence interval (see chapter 8) is \((0.0676, 0.2297)\).

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

Registered nurses earned an average annual salary of $69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was $71,121 with a sample standard deviation of $7,489. Conduct a hypothesis test.

• \(H_{0}: \mu = 69,110\)
• \(H_{0}: \mu > 69,110\)
• Let \(\bar{X} =\) the mean salary in dollars for California registered nurses.
• \(t = 1.719\)
• \(p\text{-value}: 0.0466\)
• Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the mean salary of California registered nurses exceeds $69,110.
• \(($68,757, $73,485)\)

La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five worldwide. In America, most nursing mothers wean their children much earlier. Suppose a random survey is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was nine months (3/4 year) with a standard deviation of 4 months. Conduct a hypothesis test to determine if the mean weaning age in the U.S. is less than four years old.

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

• Reject \(H_{0}\): There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
• Do not reject \(H_{0}\): There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.
• Do not reject \(H_{0}\): There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.
• Reject \(H_{0}\): There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing.

At a 1% level of significance, an appropriate conclusion is:

• There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.
• There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is more than 20%.
• There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.
• There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is at least 20%.

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

At a significance level of \(a = 0.05\), what is the correct conclusion?

• There is enough evidence to conclude that the mean number of hours is more than 4.75
• There is enough evidence to conclude that the mean number of hours is more than 4.5
• There is not enough evidence to conclude that the mean number of hours is more than 4.5
• There is not enough evidence to conclude that the mean number of hours is more than 4.75

Instructions: For the following ten exercises,

Hypothesis testing: For the following ten exercises, answer each question.

State the null and alternate hypothesis.

State the \(p\text{-value}\).

State \(\alpha\).

What is your decision?

Write a conclusion.

Answer any other questions asked in the problem.

According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

• \(H_{0}: p = 0.488\) \(H_{a}: p \neq 0.488\)
• \(p\text{-value} = 0.0114\)
• \(\alpha = 0.05\)
• Reject the null hypothesis.
• At the 5% level of significance, there is enough evidence to conclude that 48.8% of families own stocks.
• The survey does not appear to be accurate.

Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. Using \(\alpha = 0.05\), is the AAA proportion accurate?

The US Department of Energy reported that 51.7% of homes were heated by natural gas. A random sample of 221 homes in Kentucky found that 115 were heated by natural gas. Does the evidence support the claim for Kentucky at the \(\alpha = 0.05\) level in Kentucky? Are the results applicable across the country? Why?

• \(H_{0}: p = 0.517\) \(H_{0}: p \neq 0.517\)
• \(p\text{-value} = 0.9203\).
• \(\alpha = 0.05\).
• Do not reject the null hypothesis.
• At the 5% significance level, there is not enough evidence to conclude that the proportion of homes in Kentucky that are heated by natural gas is 0.517.
• However, we cannot generalize this result to the entire nation. First, the sample’s population is only the state of Kentucky. Second, it is reasonable to assume that homes in the extreme north and south will have extreme high usage and low usage, respectively. We would need to expand our sample base to include these possibilities if we wanted to generalize this claim to the entire nation.

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected 100 patrons and found that 82 borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use \(\alpha = 0.01\) level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the \(\alpha = 0.05 level\), can it be concluded that the mean rainfall was below the reported average? What if \(\alpha = 0.01\)? Assume the amount of summer rainfall follows a normal distribution.

• \(H_{0}: \mu \geq 11.52\) \(H_{a}: \mu < 11.52\)
• \(p\text{-value} = 0.000002\) which is almost 0.
• At the 5% significance level, there is enough evidence to conclude that the mean amount of summer rain in the northeaster US is less than 11.52 inches, on average.
• We would make the same conclusion if alpha was 1% because the \(p\text{-value}\) is almost 0.

A survey in the N.Y. Times Almanac finds the mean commute time (one way) is 25.4 minutes for the 15 largest US cities. The Austin, TX chamber of commerce feels that Austin’s commute time is less and wants to publicize this fact. The mean for 25 randomly selected commuters is 22.1 minutes with a standard deviation of 5.3 minutes. At the \(\alpha = 0.10\) level, is the Austin, TX commute significantly less than the mean commute time for the 15 largest US cities?

A report by the Gallup Poll found that a woman visits her doctor, on average, at most 5.8 times each year. A random sample of 20 women results in these yearly visit totals

3; 2; 1; 3; 7; 2; 9; 4; 6; 6; 8; 0; 5; 6; 4; 2; 1; 3; 4; 1

At the \(\alpha = 0.05\) level can it be concluded that the sample mean is higher than 5.8 visits per year?

• \(H_{0}: \mu \leq 5.8\) \(H_{a}: \mu > 5.8\)
• \(p\text{-value} = 0.9987\)
• At the 5% level of significance, there is not enough evidence to conclude that a woman visits her doctor, on average, more than 5.8 times a year.

According to the N.Y. Times Almanac the mean family size in the U.S. is 3.18. A sample of a college math class resulted in the following family sizes:

5; 4; 5; 4; 4; 3; 6; 4; 3; 3; 5; 5; 6; 3; 3; 2; 7; 4; 5; 2; 2; 2; 3; 2

At \(\alpha = 0.05\) level, is the class’ mean family size greater than the national average? Does the Almanac result remain valid? Why?

The student academic group on a college campus claims that freshman students study at least 2.5 hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standard deviation of 45 minutes. At α = 0.01 level, is the student academic group’s claim correct?

• \(H_{0}: \mu \geq 150\) \(H_{0}: \mu < 150\)
• \(p\text{-value} = 0.0622\)
• \(\alpha = 0.01\)
• At the 1% significance level, there is not enough evidence to conclude that freshmen students study less than 2.5 hours per day, on average.
• The student academic group’s claim appears to be correct.

9.7: Hypothesis Testing of a Single Mean and Single Proportion

Read our research on: Gun Policy | International Conflict | Election 2024

Regions & Countries

6. teachers’ views on the state of public k-12 education.

Overall, teachers have a negative view of the U.S. K-12 education system – both the path it’s been on in recent years and what its future might hold.

The vast majority of teachers (82%) say that the overall state of public K-12 education has gotten worse in the last five years. Only 5% say it’s gotten better, and 11% say it has gotten neither better nor worse.

Looking to the future, 53% of teachers expect the state of public K-12 education to be worse five years from now. One-in-five say it will get better, and 16% expect it to be neither better nor worse.

We asked teachers who say the state of public K-12 education is worse now than it was five years ago how much each of the following has contributed:

• The current political climate (60% of teachers say this is a major reason that the state of K-12 education has gotten worse)
• The lasting effects of the COVID-19 pandemic (57%)
• Changes in the availability of funding and resources (46%)

Elementary school teachers are especially likely to point to resource issues – 54% say changes in the availability of funding and resources is a major reason the K-12 education system is worse now. By comparison, 41% of middle school and 39% of high school teachers say the same.

Differences by party

Overall, teachers who are Democrats and Democratic-leaning independents are as likely as Republican and Republican-leaning teachers to say that the state of public K-12 education is worse than it was five years ago.

But Democratic teachers are more likely than Republican teachers to point to the current political climate (65% vs. 54%) and changes in the availability of funding and resources (50% vs. 40%) as major reasons.

Democratic and Republican teachers are equally likely to say that lasting effects of the pandemic are a major reason that the public K-12 education is worse than it was five years ago (57% each).

K-12 education and political parties

We asked teachers which political party they trust to do a better job on various aspects of public K-12 education.

Across each of the issues we asked about, roughly a third or more of teachers say they don’t trust either party to do a better job. In particular, a sizable share (42%) trust neither party when it comes to shaping the school curriculum.

On balance, more teachers say they trust the Democratic Party to do a better job handling the things we asked about than say they trust the Republican Party.

About a third of teachers say they trust the Democratic Party to do a better job in ensuring adequate funding for schools, adequate pay and benefits for teachers, and equal access to high quality K-12 education for students. Only about one-in-ten teachers say they trust the Republican Party to do a better job in these areas.

A quarter of teachers say they trust the Democratic Party to do a better job in shaping the school curriculum and making schools safer; 11% and 16% of teachers, respectively, say they trust the Republican Party in these areas.

Across all the items we asked about, shares ranging from 15% to 17% say they are not sure which party they trust more, and shares ranging from 4% to 7% say they trust both parties equally.

A majority of public K-12 teachers (58%) identify with or lean toward the Democratic Party. About a third (35%) identify with or lean toward the GOP.

For each aspect of the education system we asked about, both Democratic and Republican teachers are more likely to say they trust their own party to do a better job than to say they trust the other party.

However, across most of these areas, Republican teachers are more likely to say they trust neither party than to say they trust their own party.

For example, about four-in-ten Republican teachers say they trust neither party when it comes to ensuring adequate funding for schools and equal access to high quality K-12 education for students. Only about a quarter of Republican teachers say they trust their own party on these issues.

The noteworthy exception is making schools safer, where similar shares of Republican teachers trust their own party (41%) and neither party (35%) to do a better job.

Social Trends Monthly Newsletter

Sign up to to receive a monthly digest of the Center's latest research on the attitudes and behaviors of Americans in key realms of daily life

Report Materials

Table of contents, ‘back to school’ means anytime from late july to after labor day, depending on where in the u.s. you live, among many u.s. children, reading for fun has become less common, federal data shows, most european students learn english in school, for u.s. teens today, summer means more schooling and less leisure time than in the past, about one-in-six u.s. teachers work second jobs – and not just in the summer, most popular.

About Pew Research Center Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of The Pew Charitable Trusts .