   # Consider the following hypothesis test. H 0 : μ ≥ 10 H a : μ &lt; 10 The sample size is 120 and the population standard deviation is 5. Use α = .05. If the actual population mean is 9, the probability of a Type II error is .2912. Suppose the researcher wants to reduce the probability of a Type II error to .10 when the actual population mean is 9. What sample size is recommended? 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 9.7, Problem 54E
Textbook Problem
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## Consider the following hypothesis test. H0: μ ≥ 10 Ha: μ < 10 The sample size is 120 and the population standard deviation is 5. Use α = .05. If the actual population mean is 9, the probability of a Type II error is .2912. Suppose the researcher wants to reduce the probability of a Type II error to .10 when the actual population mean is 9. What sample size is recommended?

To determine

Find the sample size.

### Explanation of Solution

Calculation:

The given information is that β=0.10, Power=0.90(=10.10), σ=5, μa=9 and μ0=10.

The null and alternative hypotheses are given below:

Null hypothesis:

H0:μ10

Alternative hypothesis:

Ha

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