Explanation Given: According to the example 7.9, the power of the test is given as 89% for n = 20 . And the value of test statistic is 0.580. The value of n is considered as 25. Calculation: The value of sample t can be calculated as: t = x ¯ s / n The value of t * at 25 − 1 = 24 degrees of freedom and 5% significance level is obtained from the t -distribution table as 1.711. So, the value of x ¯ can be calculated as: t ≥ t * x ¯ s / n ≥ 1.711 x ¯ ≥ 1.711 × 1.5 25 x ¯ ≥ 0.5133 The power of test for the provided case can be calculated as: P ( x ¯ ≥ 0.5133 ) = P ( Z ≥ x ¯ − μ s / n ) = P ( Z ≥ 0

8th Edition

ISBN: 9781319116828

Author: Moore

Publisher: VST

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Chapter 7.1, Problem 15UYK

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EBK INTRODUCTION TO THE PRACTICE OF STA

Ch. 7.1 - Prob. 1UYK Ch. 7.1 - Prob. 2UYK Ch. 7.1 - Prob. 3UYK Ch. 7.1 - Prob. 4UYK Ch. 7.1 - Prob. 5UYK Ch. 7.1 - Prob. 6UYK Ch. 7.1 - Prob. 7UYK Ch. 7.1 - Prob. 8UYK Ch. 7.1 - Prob. 9UYK Ch. 7.1 - Prob. 10UYK

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The effect on power of the test by changing the sample size .

Solution Summary: The author explains how the power of the test increases when the sample size is increased to 25 from 20.

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