1. What are the conditions required for performing the Wilcoxon signed rank test? (p. 14-21

2. Describe what is meant by a symmetric distribution. (p. 14-18

3. Explain the boxplot criterion for assessing symmetry. (p. 14-19

4. Describe how the Wilcoxon signed rank test takes the magnitude of the data into account. (p. 14-20

5. What are the four steps involved (a–d) in calculating the signed ranks of the data? (p. 14-21

6. State the three ways in which the Wilcoxon signed rank test for the population median is comparable to the sign test for the population median. (p. 14-24

7. For each of the right-tailed test, the left-tailed test, and the two-tailed test, state what the test statistic equals. (p. 14-22

8. Explain how ties are resolved when calculating ranks. (p. 14-21

9. State the rejection rule for the Wilcoxon signed rank test for the small-sample case. Do the same for the large-sample case. (p. 14-21

10. We may use the same methods for the Wilcoxon signed rank test for matched-pair data that we use for the Wilcoxon signed rank test for a single population median, except that we must do one extra step. What is that step? (p. 14-23

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23. Women's Body Temperatures. Use the following random sample of seven women's body temperatures to test, using the Wilcoxon signed rank test, whether the population median of women's body temperatures differs from 98.6 degrees Fahrenheit.⁴

The accompanying figure is a boxplot of the data. Use level of significance .

24. Earthquake Magnitudes. The following data from the U.S. Geological Survey represent the magnitude on the Richter scale of a random sample of 10 earthquakes worldwide that occurred during the week of August 3, 2014.

The accompanying figure is a boxplot of the data. Use the Wilcoxon signed rank test to test whether the population median magnitude of earthquakes is less than 6.0. Use level of significance .

25. Small Businesses. The following data set represents the number of businesses in a random sample of eight cities nationwide.⁵

The accompanying figure is a boxplot of the data. Test, using the Wilcoxon signed rank test, whether the population median number of businesses per city is greater than 2500, using level of significance .

26. Outliers: Muscular Endurance. The muscular endurance of 15 randomly selected males was measured after taking a single 600-milligram dose of vitamin C and also after taking a sugar placebo. Muscular endurance was measured by repetitive grip strength.⁶ The following data set represents the differences in muscular endurance (vitamin C – placebo).

The accompanying figure is a boxplot of the data. Note that the Wilcoxon signed rank test is a robust method (see Section 3.6 for similar robust methods) and is insensitive to the presence of the outlier indicated in the boxplot. In other words, the presence of a reasonable number of outliers does not impair the performance of the Wilcoxon signed rank test. Perform the Wilcoxon signed rank test at level of significance to determine whether the population median of the differences (vitamin C – placebo) differs from zero.

27. Reiki Touch Therapy. A study was performed to determine whether Reiki touch therapy was useful in the reduction of chronic pain, including that suffered by cancer patients.⁷ The pain levels reported by a random sample of 13 patients before and after Reiki touch therapy are shown here in Table 12.

Test, using the Wilcoxon signed rank test, whether there was a reduction in mean pain level after the Reiki therapy, using level of significance . The accompanying figure is a boxplot of the data.

28. Video Game Ratings. GameRankings.com publishes summary statistics for reviews of video games. The following data set represents a random sample of video games, with their average reviewer score for the PlayStation 3 platform and the Xbox 360 platform, as of January 23, 2009. Test whether the population median of the differences (PlayStation 3 – Xbox 360) is less than zero, using level of significance .