(a) In the case of the simple (one parameter) Normal model, explain how the sampling distribution of the test statistic n(Xn0) changes when evaluated

(a) In the case of the simple (one parameter) Normal model, explain how the sampling distribution of the test statistic √n(Xn−μ0)

σ changes when evaluated under the null and under the alternative: H0: μ = μ0, vs. H1: μ>μ0.

(b) In the context of the simple (one parameter) Normal model (σ = 1), test these hypotheses for μ0 = .5, xn = .789, n = 100, and α = .025, using the optimal N-P test.

(c) Evaluate the power of the optimal N-P test in

(b) for μ1 = .51, .7, 1 and plot the power curve.

(d) Evaluate how large the sample size n needs to be for one to be able to detect the discrepancy of interest μ1 − μ0 =.2 with probability ≥ .8.