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13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 9.6, Problem 47E

Textbook Problem

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Consider the following hypothesis test.

*H*_{0}: *μ* = 20

*H*_{a}: *μ* ≠ 20

A sample of 200 items will be taken and the population standard deviation is *σ =* 10.Use *α =* .05. Compute the probability of making a Type II error if the population mean is:

- a.
*μ =*18.0 - b.
*μ =*22.5 - c.
*μ =*21.0

**a.**

To determine

Find the probability of making a Type II error if

**Calculation:**

The given information is that

The test hypotheses are given below:

*Null hypothesis:*

*Alternative hypothesis:*

The rejection rule for two tailed test using the critical value is,

If

*Critical value:*

**Software Procedure:**

Step-by-step procedure to obtain the critical value using the MINITAB software:

- Choose
**Graph > Probability Distribution Plot**choose**View Probability> OK.** - From
**Distribution**, choose ‘**Normal**’ distribution. - Click the
**Shaded Area**tab. - Choose
**Probability Value**and**Both Tails**for the region of the curve to shade. - Enter the
**Probability value**as 0.05. - Click
**OK**.

Output using the MINITAB software is given below:

From the output, the critical values are

*Rejection rule:*

If

The value

**b.**

To determine

Find the probability of making a Type II error if

**c.**

To determine

Find the probability of making a Type II error if

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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