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Hypothesis Testing for Two Samples

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In this problem set you will get some practice performing hypothesis tests for two samples. If you use Statdisk to perform any portion of these analyses, please include the results, label them, and refer to them accordingly in your interpretations. Good luck and enjoy!

1. Ten infants are involved in a study to compare the effectiveness of two medications for the treatment of diaper rash. For each baby, two areas of approximately the same size and rash severity were selected and one area was treated with medication A and the other with medication B. The number of hours for the rash to disappear was recorded for each medication and each infant. The times appear below. The goal of the study is to determine whether there is enough evidence to conclude that a significant difference exists in the average time required to eliminate the rash using both hypothesis testing and a confidence interval.

A 46 50 46 51 43 45 47 48 46 48
B 43 49 48 47 40 40 47 48 46 48

1. What are the null and alternate hypotheses for this test? Why?
2. What is the critical value for this hypothesis test using a 1% significance level?
3. Calculate the test statistic and the p-value using a 1% significance level.
4. State the decision for this test.
5. Determine the confidence interval level that would be associated with this hypothesis test at the 1% significance level. Explain why the confidence interval level is appropriate for this hypothesis test at the 1% significance level.
6. Create a confidence interval at the confidence level associated with the hypothesis test above.
7. Interpret this confidence interval.
8. Is there sufficient evidence to conclude that a difference exists in the average time required to eliminate the rash at the 1% significance level? Explain this using the results from both the confidence interval and the hypothesis test.

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25. The management of Discount Furniture, a chain of discount furniture stores in the Northeast,
designed an incentive plan for salespeople. To evaluate this innovative plan, 12
salespeople were selected at random, and their weekly incomes before and after the plan
were recorded.

9. A real estate developer is considering investing in a shopping mall on the outskirts of
Atlanta, Georgia. Three parcels of land are being evaluated. Of particular importance is the
income in the area surrounding the proposed mall. A random sample of four families is
selected near each proposed mall. Following are the sample results. At the .05 significance
level, can the developer conclude there is a difference in the mean income? Use the usual
five-step hypothesis testing procedure.

12. Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

a. State the null hypothesis and the alternate hypothesis.
b. What is the decision rule?

c. Compute SST, SSE, and SS total.
d. Complete an ANOVA table.

e. State your decision regarding the null hypothesis.

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