Suppose that four observations are taken at random from the normal distribution with unknown mean and

Question:

Suppose that four observations are taken at random from the normal with unknown mean μ and known variance 1. Suppose also that the following hypotheses are to be tested:
H0: μ ≥ 10,
H1: μ<10.
a. Determine a UMP test at the level of significance α0 = 0.1.
b. Determine the power of this test when μ = 9.
c. Determine the probability of not rejecting H0 if μ = 11. Distribution
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