Problem 5BSC

Using the Wilcoxon Signed-Ranks Test.Refer to the sample data for the given exercise .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

Use the sign test for the data consisting of matched pairs.

Oscar WinnersListed below are ages of actresses and actors at the times that they won Oscars. These 10 matched pairs are the first 10 from Data Set 11 in Appendix B. The data are paired according to the years that they won. Use a 0.05 significance level to test the claim that there is no difference between the ages of best actresses and the ages of best actors at the time that the awards were presented.

Solution 5BSC

The value of the test statistic T is equal to the smaller of the two sums.

So the value of the test statistic is 6 that is T = 6

The sample size for the Wilcoxon signed rank test is equal to the number of pairs with

d ? 0, so here n = 10.

For n = 10, with a significance of 0.05 that is the critical value is found from the table A-8 (Critical Values of T for the Wilcoxon Signed-Ranks Test) as T = 8.

As the value of the test statistic is less than the critical value, so the null hypothesis is rejected.

Thus there is a difference between the ages of the best actors and that of the best actresses. Large number of negative signs suggests that the age of the best actresses is smaller than that of the best actors.