Suppose that X1, . . . , Xn form a random sample from the uniform distribution described in Exercise 6, but suppose now that it is desired to test the following hypotheses:
H0: θ = 3,
H1: θ = 3. (9.4.15)
Consider a test procedure δ such that the hypothesis H0 is rejected if either max{X1, . . . , Xn} ≤ c1 or max{X1, . . . ,Xn} ≥ c2, and let π(θ|δ) denote the power function of δ.
a. Determine the values of the constants c1 and c2 such that π(3|δ) = 0.05 and δ is unbiased.
b. Prove that the test found in part (a) is UMP of level 0.05 for testing the hypotheses in (9.4.15).
c. Determine the values of the constants c1 and c2 such that π(3|δ) = 0.05 and δ is unbiased.