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9th Edition

David R. Anderson + 4 others

Publisher: South-Western College Pub

ISBN: 9780357045435

Chapter 9.8, Problem 54E

Textbook Problem

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Consider the following hypothesis test.

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.

**Calculation:**

It is given that

The null and alternative hypotheses are given below:

*Null hypothesis:*

*Alternative hypothesis:*

*Sample size:*

The formula for finding the sample size is as follows:

Here, *z*-value providing an area of *z*-value providing an area of

*For* *:*

It is given that

The cumulative area to the left is as follows:

*Critical value:*

Use “Table 1: Cumulative probabilities for the standard normal distribution” to find

Essentials Of Statistics For Business & Economics

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