Question: Let X1,..., Xn be a random sample from a n(,2) population, 2 known. An LRT of H0: = 0 versus H1: 0 is

Let X1,..., Xn be a random sample from a n(θ,σ2) population, σ2 known. An LRT of H0: θ = θ0 versus H1: ≠ θ0 is a test that rejects H0 if | - θ0 | / (σ / √n) > c.
(a) Find an expression, in terms of standard normal probabilities, for the power function of this test.
(b) The experimenter desires a Type I Error probability of .05 and a maximum Type II Error probability of .25 at θ = θ0 + σ. Find values of n and c that will achieve this.

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