Chapter 5: Problem 13
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 \(C=\\{y: y \geq 13\\}\). (a) Determine \(\alpha=P(Y \geq 13 ; ; p=0.40)\). (b) Find \(\beta=P(Y<13)\) when \(p=0.60\); that is, \(\beta=P(Y \leq 12 ; p=0.60)\) so that \(1-\beta\) is the power at \(p=0.60\).
Short Answer
Step by step solution
Key Concepts
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