Specify the test statistic and the rejection region for the Wilcoxon rank sum test for independent samples in each of the following situations:

a. n, = 10, n, = 6, a = .10 H,: Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the right or left of the probability distribution

,, for population 2

-t;

b. n, = 5, n, = 7, a = .05 H,,: Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the right of the probability distribution for population 2 c n, = 9, n, = 8, a = .025 H,:Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the left of the probability distribution for population 2

d. n, = 15, n, = 15, a = .05 Ho:Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the right or left of the probability distribution for population 2 754 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 a test of the hypotheses described in part

a. Test using a = .05.

kd LM7-54.DAT ........................................................................................

Sample A: 37,40,33,29,42,33, 35, 28, 34 Sample B: 65,35,47,52