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

QUESTION:

Let X1, X2, ... , Xn be a random sample from the normal distribution N(, 9). To test the hypothesis H0: = 80 against H1: = 80, consider the following three critical regions: C1 = {x : x c1}, C2 = {x : x c2}, and C3 = {x: |x 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 0.05 = P(X C1; = 80) = P(X C2; = 80) = P(X C3; = 80). (b) On the same graph paper, sketch the power functions for these three critical regions.