hypothesis testing for the mean worksheet

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: H0: ˉx = 4.5, Ha: ˉx > 4.5. H0: μ ≥ 4.5, Ha: μ < 4.5. H0: μ = 4.75, Ha: μ > 4.75.

Solution: The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below: State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

8.4.3 Hypothesis Testing for the Mean. Here, we would like to discuss some common hypothesis testing problems. We assume that we have a random sample X1, X2 ,..., Xn from a distribution and our goal is to make inference about the mean of the distribution μ. We consider three hypothesis testing problems.

ONE4 SAMPLE HYPOTHESIS TESTS WORKSHEET MTH 3210 (8)A simple random sample of 21 chihuahua dog weights yields a sample mean of 5.6 pounds. It is known that the standard deviation of the population of all chihuahua weights is 1.8 pounds. Test the null hypothesis that the mean weight of all chihuahuas is 4.6 pounds at the = :1 signi cance level.

Thus the test statistic is T = ˉx − μ0 s / √n and has the Student t -distribution with n − 1 = 5 − 1 = 4 degrees of freedom. Step 3. From the data we compute ˉx = 169 and s = 10.39. Inserting these values into the formula for the test statistic gives T = ˉx − μ0 s / √n = 169 − 179 10.39 / √5 = − 2.152. Step 4.

In the next section, we set up the six steps for a hypothesis test for one mean. Objectives Upon successful completion of this lesson, you should be able to: Perform hypothesis testing for a population mean using the p-value approach and the rejection region approach. Use confidence intervals to draw conclusions about two-sided tests. ...

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.

Unit test. Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Learn how to conduct significance tests and calculate p-values to see how likely a sample result is to occur by random chance. You'll also see how we use p-values to make conclusions about hypotheses.

Using your class as the sample, conduct a hypothesis test to determine if the percent of the students at your school who speak a language other than English at home is different from 42.3%. Determine the test statistic using your data. Draw a graph and label it appropriately. Shade the actual level of significance.

5.3 - Hypothesis Testing for One-Sample Mean. In the previous section, we learned how to perform a hypothesis test for one proportion. The concepts of hypothesis testing remain constant for any hypothesis test. In these next few sections, we will present the hypothesis test for one mean. We start with our knowledge of the sampling distribution ...

This lecture explains how to conduct hypothesis tests about the mean of a normal distribution. We tackle two different cases: when we know the variance of the distribution, then we use a z-statistic to conduct the test; when the variance is unknown, then we use the t-statistic. In each case we derive the power and the size of the test.

The mean pregnancy length is 266 days. We test the following hypotheses. H 0: μ = 266. H a: μ < 266. Suppose a random sample of 40 women who smoke during their pregnancy have a mean pregnancy length of 260 days with a standard deviation of 21 days. The P-value is 0.04.

Two Types of Errors. The format of the testing procedure in general terms is to take a sample and use the information it contains to come to a decision about the two hypotheses. As stated before our decision will always be either. reject the null hypothesis \ (H_0\) in favor of the alternative \ (H_a\) presented, or.

Why do hypothesis testing? Sample mean may be di↵erent from the population mean. Type of Test to Apply: Rightailed T. µ>kuYo believe that µ is more than value stated in H 0. Left-Tailed. µ<kuYo believe that µ is less than value stated in H. 0 Two-Tailed. µ 6= k You believe that µ is di↵erent from the value stated in H. 0. Test µ When ...

We then determine the appropriate test statistic (Step 2) for the hypothesis test. The formula for the test statistic is given below. Test Statistic for Testing H0: p = p 0. if min (np 0 , n (1-p 0 )) > 5. The formula above is appropriate for large samples, defined when the smaller of np 0 and n (1-p 0) is at least 5.

7 b) Carry out a test to investigate the researchers' question. Step 1: State the claim and its opposite. Identify which is the null hypothesis and which is the alternative hypothesis. Step 2: Determine which hypothesis test you will use and check conditions. Step 3: If the conditions are met, perform the calculations and conduct the test. Step 4: State the result and interpret your result ...

The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be?

hypothesis, H 0. p-value Probability of obtaining a sample "more extreme" than the ones observed in your data, assuming H 0 is true. Hypothesis A premise or claim that we want to test. Null Hypothesis: H 0 Currently accepted value for a parameter (middle of the distribution). Is assumed true for the purpose of carrying out the hypothesis test.

Effect size. Significance tests inform us about the likelihood of a meaningful difference between groups, but they don't always tell us the magnitude of that difference. Because any difference will become "significant" with an arbitrarily large sample, it's important to quantify the effect size that you observe.

HYPOTHESIS4 TESTS FOR ONE POPULATION MEAN WORKSHEET MTH 1210, SPRING 2019 (8)A simple random sample of 21 chihuahua dog weights yields a sample mean of 5.6 pounds. It is known that the standard deviation of the population of all chihuahua weights is 1.8 pounds. Test the null hypothesis that the mean weight of all chihuahuas

Language Survey. About 42.3% of Californians and 19.6% of all Americans over age five speak a language other than English at home. Using your class as the sample, conduct a hypothesis test to determine if the percent of the students at your school who speak a language other than English at home is different from 42.3%.

The test statistic is used to decide the outcome of the hypothesis test. The test statistic is a standardized value calculated from the sample. The formula for the test statistic (TS) of a population mean is: x ¯ − μ s ⋅ n. x ¯ − μ is the difference between the sample mean ( x ¯) and the claimed population mean ( μ ).

Hypothesis Testing for Means. Hypothesis Testing, the z-Test (Activity 10) Use a z-test to determine whether the students in a school have above-average intelligence. View activity (PDF) Hypothesis Testing, the t-Test (Activity 11) Examine whether the differences between measurements of the Earth´s rotation angle reveal a real change or ...