Suppose we wish to test the hypothesis H0: = 85 versus the alternative H1: > 85 where

Question:

Suppose we wish to test the hypothesis H0: μ = 85 versus the alternative H1: μ > 85 where σ = 16. Suppose that the true mean is μ = 86 and that in the practical context of the problem this is not a departure from μ = 85 that has practical significance.
(a) For a test with a = 0.01, compute B for the sample sizes n = 25, 100, 400, and 2500 assuming that μ = 86.
(b) Suppose the sample average is = 86. Find the P-value for the test statistic for the different sample sizes specified in part (a). Would the data be statistically significant at a = 0.01?
(c) Comment on the use of a large sample size in this problem.