The rank-sum test is sometimes thought of as a test for population medians. Under the assumptions of equal spread and shape, the means of two populations will differ if and only if the medians differ; therefore tests for equality of population means are also tests for equality of population medians. This exercise illustrates that when these assumptions are seriously violated, the rank-sum test can give misleading results concerning the equality of population medians. Consider the following two samples:

a. Show that both samples have the same median.
b. Compute the P-value for a two-tailed rank-sum test. If small P-values provide evidence against the null hypothesis that the population medians are equal, would you conclude that the population medians are different?
c. Do the assumptions of the rank-sum test appear to be satisfied? Explain why or why not.

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