Problem 8.58 Let X be the sample total from a random sample of size n = 20 from a Bernoulli distribution with parameter p. To test H0 : p ≤ 0.40 against H1 : p > 0.40, we choose the rejection region C = {x : x>c}.

(a) Find the value of c such that the type I error probability α ≤ 0.05. What is the type II error if, in fact, p = 0.7?

(b) Find the value of c such that the type I error probability α ≤ 0.1. What is the type II error if, in fact, p = 0.7?