Question: Problem 8.8 Suppose we use a sample of size n = 25 taken from a normal distribution with a 10 and the rejection region C

Problem 8.8 Suppose we use a sample of size n = 25 taken from a normal distribution with a 10 and the rejection region C = {T T c} to test the hypothesis Ho:

15 against H1 : µ < 15.

(a) Find the cutoff value c so that the test has significance level α = 0.1. Compute the probability of a type II error at the alternative µ = 12.5. Hint: Use Equation 8.9.

(b) Find the cutoff value c so that the test has significance level α = 0.05. Compute the probability of a type II error at the alternative µ = 12.5. Compare the type I and type II errors of this test with the test of part (a). Discuss your conclusions.

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