Each of a group of 20 intermediate tennis players is giventwo rackets, one having nylon

Chapter 8, Problem 44

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Each of a group of 20 intermediate tennis players is giventwo rackets, one having nylon strings and the other synthetic gut strings. After several weeks of playing with the tworackets, each player will be asked to state a preference forone of the two types of strings. Let p denote the proportionof all such players who would prefer gut to nylon, and let Xbe the number of players in the sample who prefer gut.Because gut strings are more expensive, consider the nullhypothesis that at most 50% of all such players prefer gut.We simplify this to , planning to reject H0 only ifsample evidence strongly favors gut strings.a. Which of the rejection regions {15, 16, 17, 18, 19, 20},{0, 1, 2, 3, 4, 5}, or {0, 1, 2, 3, 17, 18, 19, 20} is mostappropriate, and why are the other two not appropriate?b. What is the probability of a type I error for the chosenregion of part (a)? Does the region specify a level .05test? Is it the best level .05 test?c. If 60% of all enthusiasts prefer gut, calculate the probabilityof a type II error using the appropriate region frompart (a). Repeat if 80% of all enthusiasts prefer gut.d. If 13 out of the 20 players prefer gut, should H0 berejected using a significance level of .10?