Let p denote the probability that, for a particular tennis player, the first serve is good. Since p = 0.40, this player decided to take lessons in order to increase p. When the lessons are completed, the hypothesis H0: p = 0.40 will be tested against H1: p > 0.40 on the basis of n = 25 trials. Let y equal the number of first serves that are good, and let the critical region be defined by C = {y : y ≥ 13}.
(a) Determine α = P(Y ≥ 13; p = 0.40). Use Table II in the appendix.
(b) Find β = P(Y < 13) when p = 0.60; that is, β = P(Y ≤ 12; p = 0.60).