For testing H0: p = 1 / 3 (astrologers randomly guessing) against Ha: p > 1 / 3 with n = 116, Example 13 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.
a. Show that P(Type II error) = 0.89.
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.