Let Y1, Y2, . . . , Y20 be a random sample of size n = 20 from a
normal distribution with unknown mean µ and known variance σ 2 = 5.
We want to test H0; µ = 7 vs. Ha : µ > 7. (a) Find the uniformly
most powerful test with significance level 0.05. (b) For the test
in (a), find the power at each of the following alternative values
of µ: µa = 7.5, 8.0, 8.5,...