   # Consider the following hypothesis test: H 0 : μ = 22 H a : μ ≠ 22 A sample of 75 is used and the population standard deviation is 10. Compute the p -value and state your conclusion for each of the following sample results. Use α = .01. a. x ¯ = 23 b. x ¯ = 25.1 c. x ¯ = 20 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 9.3, Problem 14E
Textbook Problem
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## Consider the following hypothesis test:H0: μ = 22Ha: μ ≠ 22A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use α = .01. a. x ¯ = 23 b. x ¯ = 25.1 c. x ¯ = 20

a.

To determine

Find the p-value for x¯=23 and state the conclusion.

### Explanation of Solution

Calculation:

The given information is that the sample size is n=75, the sample mean is x¯=23, and the population standard deviation is σ=10.

The hypotheses are given below:

Null hypothesis: H0:μ=22

Alternative hypothesis: Ha:μ22

Test statistic:

Software Procedure:

Step-by-step procedure to obtain the test statistic using the MINITAB software:

• Choose Stat > Basic Statistics > 1-Sample Z.
• In Summarized data, enter the sample size as 75 and mean as 23.
• In Standard deviation, enter a value for s as 10.
• In Perform hypothesis test, enter the test mean as 22

b.

To determine

Find the p-value for x¯=25.1 and state the conclusion.

c.

To determine

Find the p-value for x¯=20 and state the conclusion.

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