Suppose You Want to Compare Two Treatments, a and B $\alpha = 0.05$

Essay

Suppose you want to compare two treatments, A and B. In particular, you wish to determine whether the distribution for population B is shifted to the right of the distribution for population A. You plan to use the Wilcoxon rank sum test.
a. Specify the null and alternative hypotheses you would test.
b. Suppose you obtained the following independent random samples of observations on experimental units subjected to the two treatments. Conduct the test of hypotheses described above, using $\alpha = 0.05$
Sample A: 1.2, 1.5, 2.3, 3.2, 3.7, 4.1
Sample B: 2.5, 2.8, 3.6, 4.2, 4.5