A consumer advocate researches the length of life between two brands of refrigerators, Brand A and Brand B. He collects data on the longevity of 40 refrigerators for Brand A and repeats the sampling for Brand B. A portion of the data is shown in the accompanying table; the full data set is on the text website, labeled Refrigerator Longevity.
a. Specify the competing hypotheses to test whether the median length of life differs between the two brands.
b. Calculate the value of the Wilcoxon rank-sum statistic W.
c. Assume that the sampling distribution of W is approximately normal; calculate the value of the test statistic Z.
d. With α = 0.05, does median longevity differ between the two brands? Explain.