Let X1, X2, . . . , Xn be a random sample from the normal distribution N(, 9). To test the hypothesis H0: =

Let X1, X2, . . . , Xn be a random sample from the normal distribution N(μ, 9). To test the hypothesis H0: μ = 80 against H1: μ ‰  80, consider the following three critical regions: C1 = {: ‰¥ C1}, C2 = {: ‰¤ C2}, and C3 = {: | ˆ’ 80| ‰¥ C3}.
(a) If n = 16, find the values of C1, C2, C3 such that the size of each critical region is 0.05. That is, find C1, C2, C3 such that

(b) On the same graph paper, sketch the power functions for these three critical regions.

0.05 = P(X E Cli = 80) = P(X E C,: = 80) P(X E C3: = 80)