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?

[DATA] Does Octane Matter? Octane is a measure of how much fuel can be compressed before it spontaneously ignites. Some people believe that higher-octane fuels result in better gas mileage for their cars. To test this claim, a researcher randomly selected 11 individuals (and their cars) to participate in the study. Each participant received 10 gallons of gas and drove his or her car on a closed course that simulated both city and highway driving. The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine whether the car was filled up with 87-octane or 92-octane fuel first, and the driver did not know which type of fuel was in the tank. The results are in the following table:

a. Why is it important that the matching be done by driver and car?

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.

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.