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 standard deviation 2, and the following simple hypotheses are to be tested:
H0: μ=−1,
H1: μ = 1.
Determine the minimum value of α(δ) + β(δ) that can be attained for each of the following values of the sample size n:
a. n = 1 b. n = 4 c. n = 16 d. n = 36 Distribution
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