The manufacturer of a hot tub is interested in testing two different heating elements for his product. The element that produces the maximum heat gain after 15 minutes would be preferable. He obtains 10 samples of each heating unit and tests each one. The heat gain after 15 minutes (in F) follows.

Unit 1: 25, 27, 29, 31, 30, 26, 24, 32, 33, 38 Unit 2: 31, 33, 32, 35, 34, 29, 38, 35, 37, 30

(a) Is there any reason to suspect that one unit is superior to the other? Use   0.05 and the Wilcoxon rank-sum test.

(b) Use the normal approximation for the Wilcoxon rank-sum test. Assume that   0.05. What is the approximate P-value for this test statistic?