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. Suppose also that the following hypotheses are to be tested:
H0: μ ≤ 0,
H1: μ > 0.
Let δ∗ denote the UMP test of these hypotheses at the level of significance α0 = 0.025, and let π(μ|δ∗) denote the power function of δ∗.
a. Determine the smallest value of the sample size n for which π(μ|δ∗) ≥ 0.9 for μ ≥ 0.5.
b. Determine the smallest value of n for which π(μ|δ∗) ≤ 0.001 for μ ≤ −0.1. Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...