Suppose that X1, . . . , Xn comprise a random sample from the normal distribution with unknown mean θ and known variance 1. Suppose that it is desired to test the same hypotheses as in Exercise 3. This time, however, the test procedure δ will be chosen so as to minimize 19π(0|δ) + 1− π(0.5|δ).
a. Find the value cn so that the test procedure δ rejects H0 if n ≥ cn for each value n = 1, n = 100, and n = 10,000.
b. For each value of n in part (a), find the size of the test procedure δ.