Suppose we wish to test the hypothesis H0:  85 versus the alternative H1:  85 where   16.

Suppose that the true mean is  86 and that in the practical context of the problem this is not a departure from 0  85 that has practical significance.

(a) For a test with   0.01, compute  for the sample sizes n  25, 100, 400, and 2500 assuming that  86.

(b) Suppose the sample average is . Find the P-value for the test statistic for the different sample sizes specified in part (a). Would the data be statistically significant at   0.01?

(c) Comment on the use of a large sample size in this problem.