13-3 Wilcoxon Signed-Ranks Test for Matched Pairs 663 Statistical Literacy and Critical Thinking 1.Is Friday the 13th Unlucky? Listed below are numbers of hospital admissions in one region due to traffic accidents on different Fridays falling on the 6th day of a month and the following 13th day of the month (based on data from “Is Friday the 13th Bad forYour Health,” by Scanlon et al., British Medical Journal, Vol. 307). Assume that we want to use the Wilcoxon signed-ranks test to test the claim of no difference between traffic accidents that occur on Friday the 6th and those that occur on the following Friday the 13th. Identify the null hypothesis and alternative hypothesis. a. What requirements must be satisfied for this test? b. Is there any requirement that the samples must be from populations having a normal distribution or any other specific distribution? c. In what sense is the Wilcoxon signed-ranks test a “distribution-free test”? Friday 6th 9 6 11 11 3 5 Friday 13th 13121410 4 12 2.Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test: a. Differences d b. The ranks corresponding to the nonzero values of d c. The signed ranks d. The sum of the positive ranks and the sum of the absolute values of the negative ranks e. The value of the test statistic T f. The critical value of T (assuming a 0.05 significance level in a test of no difference between hospital admissions of Friday 6th and the following Friday 13th). 3.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? 4. Efficiency of the Wilcoxon Signed-Ranks Test Refer to Table 13-2 on page 645 and identify the efficiency of the Wilcoxon signed-ranks test. What does that value tell us about the test? Using the Wilcoxon Signed-Ranks Test. In Exercises 5–8, refer to the sample data for the given exercises in Section 13-2 on page 656. 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. 5. Exercise 5 “Measured and Reported Weights” 6. Exercise 6 “Do Men and Women Talk the Same Amount?” 7. Exercise 7 “Do Men and Women Talk the Same Amount?” 8. Exercise 8 “Oscars” In Exercises 9–12, refer to the sample data from the given exercises in Section 13-2 on page 657. Use the Wilcoxon signed-ranks test for the claim about the median of a population. 9. Exercise 13 “Body Temperatures” 10. Exercise 14 “Peanut Butter Cups” 11. Exercise 15 “Cotinine in Smokers” 12. Exercise 16 “Tower of Terror” 13-3 Basic Skills and Concepts
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