directional hypothesis definition quizlet

Statistics Made Easy

What is a Directional Hypothesis? (Definition & Examples)

A statistical hypothesis is an assumption about a population parameter . For example, we may assume that the mean height of a male in the U.S. is 70 inches.

The assumption about the height is the statistical hypothesis and the true mean height of a male in the U.S. is the population parameter .

To test whether a statistical hypothesis about a population parameter is true, we obtain a random sample from the population and perform a hypothesis test on the sample data.

Whenever we perform a hypothesis test, we always write down a null and alternative hypothesis:

• Null Hypothesis (H 0 ): The sample data occurs purely from chance.
• Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

A hypothesis test can either contain a directional hypothesis or a non-directional hypothesis:

• Directional hypothesis: The alternative hypothesis contains the less than (“<“) or greater than (“>”) sign. This indicates that we’re testing whether or not there is a positive or negative effect.
• Non-directional hypothesis: The alternative hypothesis contains the not equal (“≠”) sign. This indicates that we’re testing whether or not there is some effect, without specifying the direction of the effect.

Note that directional hypothesis tests are also called “one-tailed” tests and non-directional hypothesis tests are also called “two-tailed” tests.

Check out the following examples to gain a better understanding of directional vs. non-directional hypothesis tests.

Example 1: Baseball Programs

A baseball coach believes a certain 4-week program will increase the mean hitting percentage of his players, which is currently 0.285.

To test this, he measures the hitting percentage of each of his players before and after participating in the program.

He then performs a hypothesis test using the following hypotheses:

• H 0 : μ = .285 (the program will have no effect on the mean hitting percentage)
• H A : μ > .285 (the program will cause mean hitting percentage to increase)

This is an example of a directional hypothesis because the alternative hypothesis contains the greater than “>” sign. The coach believes that the program will influence the mean hitting percentage of his players in a positive direction.

Example 2: Plant Growth

A biologist believes that a certain pesticide will cause plants to grow less during a one-month period than they normally do, which is currently 10 inches.

To test this, she applies the pesticide to each of the plants in her laboratory for one month.

She then performs a hypothesis test using the following hypotheses:

• H 0 : μ = 10 inches (the pesticide will have no effect on the mean plant growth)
• H A : μ < 10 inches (the pesticide will cause mean plant growth to decrease)

This is also an example of a directional hypothesis because the alternative hypothesis contains the less than “<” sign. The biologist believes that the pesticide will influence the mean plant growth in a negative direction.

Example 3: Studying Technique

A professor believes that a certain studying technique will influence the mean score that her students receive on a certain exam, but she’s unsure if it will increase or decrease the mean score, which is currently 82.

To test this, she lets each student use the studying technique for one month leading up to the exam and then administers the same exam to each of the students.

• H 0 : μ = 82 (the studying technique will have no effect on the mean exam score)
• H A : μ ≠ 82 (the studying technique will cause the mean exam score to be different than 82)

This is an example of a non-directional hypothesis because the alternative hypothesis contains the not equal “≠” sign. The professor believes that the studying technique will influence the mean exam score, but doesn’t specify whether it will cause the mean score to increase or decrease.

Additional Resources

Introduction to Hypothesis Testing Introduction to the One Sample t-test Introduction to the Two Sample t-test Introduction to the Paired Samples t-test

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Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

What is a Directional Hypothesis? (Definition & Examples)

A statistical hypothesis is an assumption about a population parameter . For example, we may assume that the mean height of a male in the U.S. is 70 inches.

The assumption about the height is the statistical hypothesis and the true mean height of a male in the U.S. is the population parameter .

To test whether a statistical hypothesis about a population parameter is true, we obtain a random sample from the population and perform a hypothesis test on the sample data.

Whenever we perform a hypothesis test, we always write down a null and alternative hypothesis:

• Null Hypothesis (H 0 ): The sample data occurs purely from chance.
• Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

A hypothesis test can either contain a directional hypothesis or a non-directional hypothesis:

• Directional hypothesis: The alternative hypothesis contains the less than (“”) sign. This indicates that we’re testing whether or not there is a positive or negative effect.
• Non-directional hypothesis: The alternative hypothesis contains the not equal (“≠”) sign. This indicates that we’re testing whether or not there is some effect, without specifying the direction of the effect.

Note that directional hypothesis tests are also called “one-tailed” tests and non-directional hypothesis tests are also called “two-tailed” tests.

Check out the following examples to gain a better understanding of directional vs. non-directional hypothesis tests.

Example 1: Baseball Programs

A baseball coach believes a certain 4-week program will increase the mean hitting percentage of his players, which is currently 0.285.

To test this, he measures the hitting percentage of each of his players before and after participating in the program.

He then performs a hypothesis test using the following hypotheses:

• H 0 : μ = .285 (the program will have no effect on the mean hitting percentage)
• H A : μ > .285 (the program will cause mean hitting percentage to increase)

This is an example of a directional hypothesis because the alternative hypothesis contains the greater than “>” sign. The coach believes that the program will influence the mean hitting percentage of his players in a positive direction.

Example 2: Plant Growth

A biologist believes that a certain pesticide will cause plants to grow less during a one-month period than they normally do, which is currently 10 inches.

To test this, she applies the pesticide to each of the plants in her laboratory for one month.

She then performs a hypothesis test using the following hypotheses:

• H 0 : μ = 10 inches (the pesticide will have no effect on the mean plant growth)

This is also an example of a directional hypothesis because the alternative hypothesis contains the less than “negative direction.

Example 3: Studying Technique

A professor believes that a certain studying technique will influence the mean score that her students receive on a certain exam, but she’s unsure if it will increase or decrease the mean score, which is currently 82.

To test this, she lets each student use the studying technique for one month leading up to the exam and then administers the same exam to each of the students.

• H 0 : μ = 82 (the studying technique will have no effect on the mean exam score)
• H A : μ ≠ 82 (the studying technique will cause the mean exam score to be different than 82)

This is an example of a non-directional hypothesis because the alternative hypothesis contains the not equal “≠” sign. The professor believes that the studying technique will influence the mean exam score, but doesn’t specify whether it will cause the mean score to increase or decrease.

Additional Resources

Introduction to Hypothesis Testing Introduction to the One Sample t-test Introduction to the Two Sample t-test Introduction to the Paired Samples t-test

How to Perform a Partial F-Test in Excel

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Directional Hypothesis: Definition and 10 Examples

A directional hypothesis refers to a type of hypothesis used in statistical testing that predicts a particular direction of the expected relationship between two variables.

In simpler terms, a directional hypothesis is an educated, specific guess about the direction of an outcome—whether an increase, decrease, or a proclaimed difference in variable sets.

For example, in a study investigating the effects of sleep deprivation on cognitive performance, a directional hypothesis might state that as sleep deprivation (Independent Variable) increases, cognitive performance (Dependent Variable) decreases (Killgore, 2010). Such a hypothesis offers a clear, directional relationship whereby a specific increase or decrease is anticipated.

Global warming provides another notable example of a directional hypothesis. A researcher might hypothesize that as carbon dioxide (CO2) levels increase, global temperatures also increase (Thompson, 2010). In this instance, the hypothesis clearly articulates an upward trend for both variables. 

In any given circumstance, it’s imperative that a directional hypothesis is grounded on solid evidence. For instance, the CO2 and global temperature relationship is based on substantial scientific evidence, and not on a random guess or mere speculation (Florides & Christodoulides, 2009).

Directional vs Non-Directional vs Null Hypotheses

A directional hypothesis is generally contrasted to a non-directional hypothesis. Here’s how they compare:

• Directional hypothesis: A directional hypothesis provides a perspective of the expected relationship between variables, predicting the direction of that relationship (either positive, negative, or a specific difference). 
• Non-directional hypothesis: A non-directional hypothesis denotes the possibility of a relationship between two variables ( the independent and dependent variables ), although this hypothesis does not venture a prediction as to the direction of this relationship (Ali & Bhaskar, 2016). For example, a non-directional hypothesis might state that there exists a relationship between a person’s diet (independent variable) and their mood (dependent variable), without indicating whether improvement in diet enhances mood positively or negatively. Overall, the choice between a directional or non-directional hypothesis depends on the known or anticipated link between the variables under consideration in research studies.

Another very important type of hypothesis that we need to know about is a null hypothesis :

• Null hypothesis : The null hypothesis stands as a universality—the hypothesis that there is no observed effect in the population under study, meaning there is no association between variables (or that the differences are down to chance). For instance, a null hypothesis could be constructed around the idea that changing diet (independent variable) has no discernible effect on a person’s mood (dependent variable) (Yan & Su, 2016). This proposition is the one that we aim to disprove in an experiment.

While directional and non-directional hypotheses involve some integrated expectations about the outcomes (either distinct direction or a vague relationship), a null hypothesis operates on the premise of negating such relationships or effects.

The null hypotheses is typically proposed to be negated or disproved by statistical tests, paving way for the acceptance of an alternate hypothesis (either directional or non-directional).

Directional Hypothesis Examples

1. exercise and heart health.

Research suggests that as regular physical exercise (independent variable) increases, the risk of heart disease (dependent variable) decreases (Jakicic, Davis, Rogers, King, Marcus, Helsel, Rickman, Wahed, Belle, 2016). In this example, a directional hypothesis anticipates that the more individuals maintain routine workouts, the lesser would be their odds of developing heart-related disorders. This assumption is based on the underlying fact that routine exercise can help reduce harmful cholesterol levels, regulate blood pressure, and bring about overall health benefits. Thus, a direction – a decrease in heart disease – is expected in relation with an increase in exercise. 

2. Screen Time and Sleep Quality

Another classic instance of a directional hypothesis can be seen in the relationship between the independent variable, screen time (especially before bed), and the dependent variable, sleep quality. This hypothesis predicts that as screen time before bed increases, sleep quality decreases (Chang, Aeschbach, Duffy, Czeisler, 2015). The reasoning behind this hypothesis is the disruptive effect of artificial light (especially blue light from screens) on melatonin production, a hormone needed to regulate sleep. As individuals spend more time exposed to screens before bed, it is predictably hypothesized that their sleep quality worsens. 

3. Job Satisfaction and Employee Turnover

A typical scenario in organizational behavior research posits that as job satisfaction (independent variable) increases, the rate of employee turnover (dependent variable) decreases (Cheng, Jiang, & Riley, 2017). This directional hypothesis emphasizes that an increased level of job satisfaction would lead to a reduced rate of employees leaving the company. The theoretical basis for this hypothesis is that satisfied employees often tend to be more committed to the organization and are less likely to seek employment elsewhere, thus reducing turnover rates.

4. Healthy Eating and Body Weight

Healthy eating, as the independent variable, is commonly thought to influence body weight, the dependent variable, in a positive way. For example, the hypothesis might state that as consumption of healthy foods increases, an individual’s body weight decreases (Framson, Kristal, Schenk, Littman, Zeliadt, & Benitez, 2009). This projection is based on the premise that healthier foods, such as fruits and vegetables, are generally lower in calories than junk food, assisting in weight management.

5. Sun Exposure and Skin Health

The association between sun exposure (independent variable) and skin health (dependent variable) allows for a definitive hypothesis declaring that as sun exposure increases, the risk of skin damage or skin cancer increases (Whiteman, Whiteman, & Green, 2001). The premise aligns with the understanding that overexposure to the sun’s ultraviolet rays can deteriorate skin health, leading to conditions like sunburn or, in extreme cases, skin cancer.

6. Study Hours and Academic Performance

A regularly assessed relationship in academia suggests that as the number of study hours (independent variable) rises, so too does academic performance (dependent variable) (Nonis, Hudson, Logan, Ford, 2013). The hypothesis proposes a positive correlation , with an increase in study time expected to contribute to enhanced academic outcomes.

7. Screen Time and Eye Strain

It’s commonly hypothesized that as screen time (independent variable) increases, the likelihood of experiencing eye strain (dependent variable) also increases (Sheppard & Wolffsohn, 2018). This is based on the idea that prolonged engagement with digital screens—computers, tablets, or mobile phones—can cause discomfort or fatigue in the eyes, attributing to symptoms of eye strain.

8. Physical Activity and Stress Levels

In the sphere of mental health, it’s often proposed that as physical activity (independent variable) increases, levels of stress (dependent variable) decrease (Stonerock, Hoffman, Smith, Blumenthal, 2015). Regular exercise is known to stimulate the production of endorphins, the body’s natural mood elevators, helping to alleviate stress.

9. Water Consumption and Kidney Health

A common health-related hypothesis might predict that as water consumption (independent variable) increases, the risk of kidney stones (dependent variable) decreases (Curhan, Willett, Knight, & Stampfer, 2004). Here, an increase in water intake is inferred to reduce the risk of kidney stones by diluting the substances that lead to stone formation.

10. Traffic Noise and Sleep Quality

In urban planning research, it’s often supposed that as traffic noise (independent variable) increases, sleep quality (dependent variable) decreases (Muzet, 2007). Increased noise levels, particularly during the night, can result in sleep disruptions, thus, leading to poor sleep quality.

11. Sugar Consumption and Dental Health

In the field of dental health, an example might be stating as one’s sugar consumption (independent variable) increases, dental health (dependent variable) decreases (Sheiham, & James, 2014). This stems from the fact that sugar is a major factor in tooth decay, and increased consumption of sugary foods or drinks leads to a decline in dental health due to the high likelihood of cavities.

See 15 More Examples of Hypotheses Here

A directional hypothesis plays a critical role in research, paving the way for specific predicted outcomes based on the relationship between two variables. These hypotheses clearly illuminate the expected direction—the increase or decrease—of an effect. From predicting the impacts of healthy eating on body weight to forecasting the influence of screen time on sleep quality, directional hypotheses allow for targeted and strategic examination of phenomena. In essence, directional hypotheses provide the crucial path for inquiry, shaping the trajectory of research studies and ultimately aiding in the generation of insightful, relevant findings.

Ali, S., & Bhaskar, S. (2016). Basic statistical tools in research and data analysis. Indian Journal of Anaesthesia, 60 (9), 662-669. doi: https://doi.org/10.4103%2F0019-5049.190623  

Chang, A. M., Aeschbach, D., Duffy, J. F., & Czeisler, C. A. (2015). Evening use of light-emitting eReaders negatively affects sleep, circadian timing, and next-morning alertness. Proceeding of the National Academy of Sciences, 112 (4), 1232-1237. doi: https://doi.org/10.1073/pnas.1418490112  

Cheng, G. H. L., Jiang, D., & Riley, J. H. (2017). Organizational commitment and intrinsic motivation of regular and contractual primary school teachers in China. New Psychology, 19 (3), 316-326. Doi: https://doi.org/10.4103%2F2249-4863.184631  

Curhan, G. C., Willett, W. C., Knight, E. L., & Stampfer, M. J. (2004). Dietary factors and the risk of incident kidney stones in younger women: Nurses’ Health Study II. Archives of Internal Medicine, 164 (8), 885–891.

Florides, G. A., & Christodoulides, P. (2009). Global warming and carbon dioxide through sciences. Environment international , 35 (2), 390-401. doi: https://doi.org/10.1016/j.envint.2008.07.007

Framson, C., Kristal, A. R., Schenk, J. M., Littman, A. J., Zeliadt, S., & Benitez, D. (2009). Development and validation of the mindful eating questionnaire. Journal of the American Dietetic Association, 109 (8), 1439-1444. doi: https://doi.org/10.1016/j.jada.2009.05.006  

Jakicic, J. M., Davis, K. K., Rogers, R. J., King, W. C., Marcus, M. D., Helsel, D., … & Belle, S. H. (2016). Effect of wearable technology combined with a lifestyle intervention on long-term weight loss: The IDEA randomized clinical trial. JAMA, 316 (11), 1161-1171.

Khan, S., & Iqbal, N. (2013). Study of the relationship between study habits and academic achievement of students: A case of SPSS model. Higher Education Studies, 3 (1), 14-26.

Killgore, W. D. (2010). Effects of sleep deprivation on cognition. Progress in brain research , 185 , 105-129. doi: https://doi.org/10.1016/B978-0-444-53702-7.00007-5  

Marczinski, C. A., & Fillmore, M. T. (2014). Dissociative antagonistic effects of caffeine on alcohol-induced impairment of behavioral control. Experimental and Clinical Psychopharmacology, 22 (4), 298–311. doi: https://psycnet.apa.org/doi/10.1037/1064-1297.11.3.228  

Muzet, A. (2007). Environmental Noise, Sleep and Health. Sleep Medicine Reviews, 11 (2), 135-142. doi: https://doi.org/10.1016/j.smrv.2006.09.001  

Nonis, S. A., Hudson, G. I., Logan, L. B., & Ford, C. W. (2013). Influence of perceived control over time on college students’ stress and stress-related outcomes. Research in Higher Education, 54 (5), 536-552. doi: https://doi.org/10.1023/A:1018753706925  

Sheiham, A., & James, W. P. (2014). A new understanding of the relationship between sugars, dental caries and fluoride use: implications for limits on sugars consumption. Public health nutrition, 17 (10), 2176-2184. Doi: https://doi.org/10.1017/S136898001400113X  

Sheppard, A. L., & Wolffsohn, J. S. (2018). Digital eye strain: prevalence, measurement and amelioration. BMJ open ophthalmology , 3 (1), e000146. doi: http://dx.doi.org/10.1136/bmjophth-2018-000146

Stonerock, G. L., Hoffman, B. M., Smith, P. J., & Blumenthal, J. A. (2015). Exercise as Treatment for Anxiety: Systematic Review and Analysis. Annals of Behavioral Medicine, 49 (4), 542–556. doi: https://doi.org/10.1007/s12160-014-9685-9  

Thompson, L. G. (2010). Climate change: The evidence and our options. The Behavior Analyst , 33 , 153-170. Doi: https://doi.org/10.1007/BF03392211  

Whiteman, D. C., Whiteman, C. A., & Green, A. C. (2001). Childhood sun exposure as a risk factor for melanoma: a systematic review of epidemiologic studies. Cancer Causes & Control, 12 (1), 69-82. doi: https://doi.org/10.1023/A:1008980919928

Yan, X., & Su, X. (2009). Linear regression analysis: theory and computing . New Jersey: World Scientific.

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Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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Directional and non-directional hypothesis: A Comprehensive Guide

Karolina Konopka

Customer support manager

In the world of research and statistical analysis, hypotheses play a crucial role in formulating and testing scientific claims. Understanding the differences between directional and non-directional hypothesis is essential for designing sound experiments and drawing accurate conclusions. Whether you’re a student, researcher, or simply curious about the foundations of hypothesis testing, this guide will equip you with the knowledge and tools to navigate this fundamental aspect of scientific inquiry.

Understanding Directional Hypothesis

Understanding directional hypotheses is crucial for conducting hypothesis-driven research, as they guide the selection of appropriate statistical tests and aid in the interpretation of results. By incorporating directional hypotheses, researchers can make more precise predictions, contribute to scientific knowledge, and advance their fields of study.

Definition of directional hypothesis

Directional hypotheses, also known as one-tailed hypotheses, are statements in research that make specific predictions about the direction of a relationship or difference between variables. Unlike non-directional hypotheses, which simply state that there is a relationship or difference without specifying its direction, directional hypotheses provide a focused and precise expectation.

A directional hypothesis predicts either a positive or negative relationship between variables or predicts that one group will perform better than another. It asserts a specific direction of effect or outcome. For example, a directional hypothesis could state that “increased exposure to sunlight will lead to an improvement in mood” or “participants who receive the experimental treatment will exhibit higher levels of cognitive performance compared to the control group.”

Directional hypotheses are formulated based on existing theory, prior research, or logical reasoning, and they guide the researcher’s expectations and analysis. They allow for more targeted predictions and enable researchers to test specific hypotheses using appropriate statistical tests.

The role of directional hypothesis in research

Directional hypotheses also play a significant role in research surveys. Let’s explore their role specifically in the context of survey research:

• Objective-driven surveys : Directional hypotheses help align survey research with specific objectives. By formulating directional hypotheses, researchers can focus on gathering data that directly addresses the predicted relationship or difference between variables of interest.
• Question design and measurement : Directional hypotheses guide the design of survey question types and the selection of appropriate measurement scales. They ensure that the questions are tailored to capture the specific aspects related to the predicted direction, enabling researchers to obtain more targeted and relevant data from survey respondents.
• Data analysis and interpretation : Directional hypotheses assist in data analysis by directing researchers towards appropriate statistical tests and methods. Researchers can analyze the survey data to specifically test the predicted relationship or difference, enhancing the accuracy and reliability of their findings. The results can then be interpreted within the context of the directional hypothesis, providing more meaningful insights.
• Practical implications and decision-making : Directional hypotheses in surveys often have practical implications. When the predicted relationship or difference is confirmed, it informs decision-making processes, program development, or interventions. The survey findings based on directional hypotheses can guide organizations, policymakers, or practitioners in making informed choices to achieve desired outcomes.
• Replication and further research : Directional hypotheses in survey research contribute to the replication and extension of studies. Researchers can replicate the survey with different populations or contexts to assess the generalizability of the predicted relationships. Furthermore, if the directional hypothesis is supported, it encourages further research to explore underlying mechanisms or boundary conditions.

By incorporating directional hypotheses in survey research, researchers can align their objectives, design effective surveys, conduct focused data analysis, and derive practical insights. They provide a framework for organizing survey research and contribute to the accumulation of knowledge in the field.

Examples of research questions for directional hypothesis

Here are some examples of research questions that lend themselves to directional hypotheses:

• Does increased daily exercise lead to a decrease in body weight among sedentary adults?
• Is there a positive relationship between study hours and academic performance among college students?
• Does exposure to violent video games result in an increase in aggressive behavior among adolescents?
• Does the implementation of a mindfulness-based intervention lead to a reduction in stress levels among working professionals?
• Is there a difference in customer satisfaction between Product A and Product B, with Product A expected to have higher satisfaction ratings?
• Does the use of social media influence self-esteem levels, with higher social media usage associated with lower self-esteem?
• Is there a negative relationship between job satisfaction and employee turnover, indicating that lower job satisfaction leads to higher turnover rates?
• Does the administration of a specific medication result in a decrease in symptoms among individuals with a particular medical condition?
• Does increased access to early childhood education lead to improved cognitive development in preschool-aged children?
• Is there a difference in purchase intention between advertisements with celebrity endorsements and advertisements without, with celebrity endorsements expected to have a higher impact?

These research questions generate specific predictions about the direction of the relationship or difference between variables and can be tested using appropriate research methods and statistical analyses.

Definition of non-directional hypothesis

Non-directional hypotheses, also known as two-tailed hypotheses, are statements in research that indicate the presence of a relationship or difference between variables without specifying the direction of the effect. Instead of making predictions about the specific direction of the relationship or difference, non-directional hypotheses simply state that there is an association or distinction between the variables of interest.

Non-directional hypotheses are often used when there is no prior theoretical basis or clear expectation about the direction of the relationship. They leave the possibility open for either a positive or negative relationship, or for both groups to differ in some way without specifying which group will perform better or worse.

Advantages and utility of non-directional hypothesis

Non-directional hypotheses in survey s offer several advantages and utilities, providing flexibility and comprehensive analysis of survey data. Here are some of the key advantages and utilities of using non-directional hypotheses in surveys:

• Exploration of Relationships : Non-directional hypotheses allow researchers to explore and examine relationships between variables without assuming a specific direction. This is particularly useful in surveys where the relationship between variables may not be well-known or there may be conflicting evidence regarding the direction of the effect.
• Flexibility in Question Design : With non-directional hypotheses, survey questions can be designed to measure the relationship between variables without being biased towards a particular outcome. This flexibility allows researchers to collect data and analyze the results more objectively.
• Open to Unexpected Findings : Non-directional hypotheses enable researchers to be open to unexpected or surprising findings in survey data. By not committing to a specific direction of the effect, researchers can identify and explore relationships that may not have been initially anticipated, leading to new insights and discoveries.
• Comprehensive Analysis : Non-directional hypotheses promote comprehensive analysis of survey data by considering the possibility of an effect in either direction. Researchers can assess the magnitude and significance of relationships without limiting their analysis to only one possible outcome.
• S tatistical Validity : Non-directional hypotheses in surveys allow for the use of two-tailed statistical tests, which provide a more conservative and robust assessment of significance. Two-tailed tests consider both positive and negative deviations from the null hypothesis, ensuring accurate and reliable statistical analysis of survey data.
• Exploratory Research : Non-directional hypotheses are particularly useful in exploratory research, where the goal is to gather initial insights and generate hypotheses. Surveys with non-directional hypotheses can help researchers explore various relationships and identify patterns that can guide further research or hypothesis development.

It is worth noting that the choice between directional and non-directional hypotheses in surveys depends on the research objectives, existing knowledge, and the specific variables being investigated. Researchers should carefully consider the advantages and limitations of each approach and select the one that aligns best with their research goals and survey design.

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Directional Hypothesis

Definition:

A directional hypothesis is a specific type of hypothesis statement in which the researcher predicts the direction or effect of the relationship between two variables.

Key Features

1. Predicts direction:

Unlike a non-directional hypothesis, which simply states that there is a relationship between two variables, a directional hypothesis specifies the expected direction of the relationship.

2. Involves one-tailed test:

Directional hypotheses typically require a one-tailed statistical test, as they are concerned with whether the relationship is positive or negative, rather than simply whether a relationship exists.

3. Example:

An example of a directional hypothesis would be: “Increasing levels of exercise will result in greater weight loss.”

4. Researcher’s prior belief:

A directional hypothesis is often formed based on the researcher’s prior knowledge, theoretical understanding, or previous empirical evidence relating to the variables under investigation.

5. Confirmatory nature:

Directional hypotheses are considered confirmatory, as they provide a specific prediction that can be tested statistically, allowing researchers to either support or reject the hypothesis.

6. Advantages and disadvantages:

Directional hypotheses help focus the research by explicitly stating the expected relationship, but they can also limit exploration of alternative explanations or unexpected findings.

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One-Tailed Test - Explained

What is a one-tailed test.

Written by Jason Gordon

Updated at April 22nd, 2024

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One-tailed test, also called directional test or directional hypothesis, is a test widely used in statistics to determine if the critical region of a distribution is in one direction, or one-sided so as to know if its value is either less or more than a specific value. If the experiment lies in the one-sided critical region, it will result in the acceptance of the alternate hypothesis, and not the null hypothesis.

How is a One-Tailed Test Used?

Hypothesis testing is a fundamental subject in inferential statistics. This test is conducted in order to ascertain the authenticity of a claim, provided a population measure. When a test aims to know if the sample mean is more than and less than the population mean, it is considered to be a two-tailed test. In contrast to this, when the experiments are performed to prove that the sample would be either more or less than the mean of a population, it is known as a one-tailed test. As this test performs experiment on one of the tails or sides of a normal distribution, it is known as a one-tailed test. Besides, the test is also applicable in other non-normal distributions. In hypothesis testing, the null and alternative hypotheses are formed prior to conducting one-tailed test. A null hypothesis involves the claim that the researcher doesnt want to go with, or wishes to reject. The alternative hypothesis involves the measurement favored by not going with the null hypothesis. In case of a financial analyst who wishes to exhibit that the portfolio manager surpassed the S&P 500 index in a specific year, he or she may consider setting up the null (H0) and alternative hypothesis (Ha) for a value, say, 16.91%. H0: 16.91 Ha: > 16.91 The value that the analyst wishes to reject is known as null hypothesis. The alternative hypothesis will be the claim that analyst makes that the performance of the portfolio manager was more than S&P 500. If the null hypothesis gets rejected in the outcome of the one-tailed tests, it will lead to the acceptance of the alternative hypothesis. However, if the outcome of the experiment cannot reject the null hypothesis, the analyst can further analyze the performance of the portfolio manager. The region of rejection for the one-tailed test is on either of the sides of the sampling distribution.

Measuring Significance

A level of significance must be mentioned in order to measure the extent of difference in returns. Probability, abbreviated as p, represents the significance level that is the probability of misinterpreting that the null hypothesis is not true. In the one-tailed test, the most commonly used significance values are 1%, 5%, or 10%. However, the analyst can use any probability determination tool as significance value. The value of probability is ascertained based on the assumption that the null hypothesis is true. This signifies that if the p-value is lower, there would be more probability that the null hypothesis is false. When the final p-value is lower than 5%, then both the observations will have a significance difference, leading the rejection of the null hypothesis. For instance, in case of p-value being 3%, the analyst will be 97% confident that the returns from portfolio were neither equivalent nor below the market returns for the given year. Hence, it will result in the rejection of H0 and will favor the claim that the portfolio manager surpassed the index. If the same tools of measurements were observed during both one-tailed and two-tailed tests, then the probability ascertained in one-tailed distribution test will be half of that of a two-tailed test. At the time of using a one-tailed test, the analyst experiments the possibility of the relationship in a single direction of interest, and discards the possibility of a relationship in any other direction. Continuing with the above example, the analyst now wants to know if the returns that a portfolio offers are more than the market returns. Also, he doesnt have to be accountable for the case where the RoI is lower than the returns offered by S&P 500 index. Thats why, analysts find using one-tailed test right only when they dont have to measure the outcome in the other direction of the distribution.

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Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

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9.1: Null and Alternative Hypotheses

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The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

\(H_0\): The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

\(H_a\): The alternative hypothesis: It is a claim about the population that is contradictory to \(H_0\) and what we conclude when we reject \(H_0\). This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject \(H_0\)" if the sample information favors the alternative hypothesis or "do not reject \(H_0\)" or "decline to reject \(H_0\)" if the sample information is insufficient to reject the null hypothesis.

\(H_{0}\) always has a symbol with an equal in it. \(H_{a}\) never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example \(\PageIndex{1}\)

• \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
• \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)

Exercise \(\PageIndex{1}\)

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

• \(H_{0}\): The drug reduces cholesterol by 25%. \(p = 0.25\)
• \(H_{a}\): The drug does not reduce cholesterol by 25%. \(p \neq 0.25\)

Example \(\PageIndex{2}\)

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

• \(H_{0}: \mu = 2.0\)
• \(H_{a}: \mu \neq 2.0\)

Exercise \(\PageIndex{2}\)

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol \((=, \neq, \geq, <, \leq, >)\) for the null and alternative hypotheses.

• \(H_{0}: \mu \_ 66\)
• \(H_{a}: \mu \_ 66\)
• \(H_{0}: \mu = 66\)
• \(H_{a}: \mu \neq 66\)

Example \(\PageIndex{3}\)

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

• \(H_{0}: \mu \geq 5\)
• \(H_{a}: \mu < 5\)

Exercise \(\PageIndex{3}\)

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• \(H_{0}: \mu \_ 45\)
• \(H_{a}: \mu \_ 45\)
• \(H_{0}: \mu \geq 45\)
• \(H_{a}: \mu < 45\)

Example \(\PageIndex{4}\)

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

• \(H_{0}: p \leq 0.066\)
• \(H_{a}: p > 0.066\)

Exercise \(\PageIndex{4}\)

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (\(=, \neq, \geq, <, \leq, >\)) for the null and alternative hypotheses.

• \(H_{0}: p \_ 0.40\)
• \(H_{a}: p \_ 0.40\)
• \(H_{0}: p = 0.40\)
• \(H_{a}: p > 0.40\)

COLLABORATIVE EXERCISE

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:

• Evaluate the null hypothesis , typically denoted with \(H_{0}\). The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality \((=, \leq \text{or} \geq)\)
• Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
• If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
• Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

\(H_{0}\) and \(H_{a}\) are contradictory.

• If \(\alpha \leq p\)-value, then do not reject \(H_{0}\).
• If\(\alpha > p\)-value, then reject \(H_{0}\).

\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .