Problem 8.2 Refer to the context of Problem 8.1. Suppose the water is regularly sampled for two weeks (so n = 14) and the observed radioactivity levels come from a normal distri[1]bution with unknown mean µ and known standard deviation σ = 0.4. The water is declared safe if x < 14.8; that is, we use the rejection region C = {x : x < 14.8} for testing the hypothesis H0 : µ ≥ 15 against H1 : µ < 15.

(a) What is the significance level of this test?

(b) Compute the probability of a type I error if, in fact, µ = 15.2.

(c) Compute the probability of a type II error if, in fact, µ = 14.9.