Suppose that X1, . . . , Xn form a random sample from the normal distribution with

Question:

Suppose that X1, . . . , Xn form a random sample from the normal with unknown mean μ and known variance 1, and it is desired to test the following hypotheses for a given number μ0:
H0: μ = μ0,
H1: μ = μ0.
Consider a test procedure δ such that the hypothesis H0 is rejected if either n ≤ c1 or n ≥ c2, and let π(μ|δ) denote the power function of δ. Determine the values of the constants c1 and c2 such that π(μ0|δ) = 0.10 and the function π(μ|δ) is symmetric with respect to the point μ = μ0.
Distribution
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