Chapter 9.6, Problem 63PB

P(Type II error) large when p close to H₀ For testing H₀: p = 1/3 (astrologers randomly guessing) against Ha: p > 1/3 with n = 116, Example 12 showed that P(Type II error) = 0.02 when p = 0.50. Now suppose that p = 0.35. Recall that P(Type I error) = 0.05.

1. a. Show that P(Type II error) = 0.89.
2. b. Explain intuitively why P(Type II error) is large when the parameter value is close to the value in H₀ and decreases as it moves farther from that value.