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13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 9.6, Problem 46E

Textbook Problem

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consider the following hypothesis test.

*H*_{0}: *μ* ≥ 10

*H*_{a}: *μ* < 10

The sample size is 120 and the population standard deviation is assumed known with *σ =* 5. Use

*α =* .05.

- a. If the population mean is 9, what is the probability that the sample mean leads to the conclusion
*do not reject H*_{0}*?* - b. What type of error would be made if the actual population mean is 9 and we conclude that
*H*≥ 10 is true?_{0}: μ - c. What is the probability of making a Type II error if the actual population mean is 8?

**a.**

To determine

Find the probability that the sample mean leads to the conclusion do not reject

**Calculation:**

The given information is that the sample size is

The hypotheses are given below:

*Null hypothesis:*

*Alternative hypothesis:*

The rejection rule for lower tail 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**Left Tail**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 value is −1.645.

*Rejection rule:*

If

The value

**b.**

To determine

Identify the type of error would be made if the actual population mean is 9 and conclude that

**c.**

To determine

Find the probability of making a Type II error if the actual population mean is 8.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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