Assume that X1, . . . , Xn are i.i.d. with the normal distribution that has mean μ and variance 1. Suppose that we wish to test the hypotheses
H0: μ ≤ μ0,
H1: μ>μ0.
Consider the test that rejectsH0 if Z ≥ c, where Z is defined in Eq. (9.1.10).
a. Show that Pr(Z ≥ c|μ) is an increasing function of μ.
b. Find c to make the test have size α0. |

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