10. Hypothesis Testing for Two Samples

Which of the following situations is a matched pairs $t$ test not an appropriate way to analyze?

When testing the difference of means for paired data, which of the following is the correct null hypothesis?

Which of the following is an example of a dependent sample suitable for analysis with the $t$-test?

Which of the following scenarios is most likely to involve dependent samples ($\mathrm{matched} \mathrm{pairs}$)?

Test the claim about the mean of the differences for a population of paired data at the level of significance α. Assume the samples are random and dependent, and the populations are normally distributed.

Claim: μd<0 , α=0.05 , Sample statistics: d̄ =1.5 , sd=3.2 , n=14

In Exercises 1–4, classify the two samples as independent or dependent and justify your answer.

Sample 1: The retail prices of 20 motorcycles

Sample 2: The retail prices of 20 minivans

Two samples are $————————————$ if the sample values are paired.

A personal trainer is studying whether a new stretching routine improves flexibility. She records the forward reach (in cm) of 6 clients before and after a 4-week program. Calculate the difference (after - before) for each client, the mean difference, and standard deviation.

Construct a 95% confidence interval for the mean difference of the population given the following information. Would you reject or fail to reject the claim that there is no difference in the mean?

$\bar{d}=-0.728$

$s_d=1.34$

$n=10$

In Exercises 17–24, use the indicated Data Sets from Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the paired sample data are simple random samples and the differences have a distribution that is approximately normal.

Heights of Presidents Repeat Exercise 12 “Heights of Presidents” using all of the sample data from Data Set 22 “Presidents” in Appendix B.

Sign Test vs. Wilcoxon Signed-Ranks Test Using the data in Exercise 1, we can test for no difference between hospital admissions on Friday 6th and Friday 13th by using the sign test or the Wilcoxon signed-ranks test. In what sense does the Wilcoxon signed-ranks test incorporate and use more information than the sign test?

Using the Wilcoxon Signed-Ranks Test

In Exercises 5–8, refer to the sample data for the given exercises in Section 13-2. Use the Wilcoxon signed-ranks test to test the claim that the matched pairs have differences that come from a population with a median equal to zero. Use a 0.05 significance level.

Exercise 6 “Do Men and Women Talk the Same Amount?”

Rank Sums Exercise 12 uses Data Set 33 “Disney World Wait Times” in Appendix B, and the sample size for the 5:00 PM Tower of Terror wait times is n = 50.

a. If we have sample paired data with 50 nonzero differences, what are the smallest and largest possible values of T?

Rank Sums Exercise 12 uses Data Set 33 “Disney World Wait Times” in Appendix B, and the sample size for the 5:00 PM Tower of Terror wait times is n = 50.

b. If we have sample paired data with 50 nonzero differences, what is the expected value of T if the population consists of matched pairs with differences having a median of 0?

Rank Sums Exercise 12 uses Data Set 33 “Disney World Wait Times” in Appendix B, and the sample size for the 5:00 PM Tower of Terror wait times is n = 50.

c. If we have sample paired data with 50 nonzero differences and the sum of the positive ranks is 165, find the absolute value of the sum of the negative ranks.