4.4-10 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 $H_0: p = 0.40$ will be tested against $H_1: p > 0.40$ based on $n = 25$ trials. Let $y$ equal the number of first serves that are good, and let the critical region be defined by $C = \{y: y \ge 13\}$.
(a) Determine $\alpha = P(Y \ge 13; p = 0.40)$. Use Table II in the Appendix.
(b) Find $\beta = P(Y < 13)$ when $p = 0.60$; that is, $\beta = P(Y \le 12; p = 0.60)$. Use Table II.
(c) What is the $p$-value associated with $y = 15$?