For testing H 0 : p = 1/3 (astrologers randomly guessing) against H a : p >

Question:

For testing H₀: p = 1/3 (astrologers randomly guessing) against H_a: 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.
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 H₀and decreases as it moves farther from that value.