Problem 8.57 Let X be the sample total from a random sample of size n = 10 from a Bernoulli distribution with parameter p. To test H0 : p ≤ 0.25 against H1 : p > 0.25, we choose the rejection region C = {x : x>c}.

(a) What is the significance level of this test for c = 4? Determine the type II error if p = 0.30, p = 0.50.

(b) What is the significance level of this test for c = 5? Determine the type II error if p = 0.30, p = 0.50.