# a. A repeated-measures study with a sample of n = 9 participants produces a mean difference of M = 3 with a standard deviation of s = 6. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with μ D = 0. b. Now assume that the sample mean difference is μ D = 12, and once again visualize the sample distribution. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with μ D = 0. c. Explain how the size of the sample mean difference influences the likelihood of finding a significant mean difference.

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570

### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570

#### Solutions

Chapter
Section
Chapter 11, Problem 7P
Textbook Problem

## a. A repeated-measures study with a sample of n = 9 participants produces a mean difference of M = 3 with a standard deviation of s = 6. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with μ D = 0.b. Now assume that the sample mean difference is μ D = 12, and once again visualize the sample distribution. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with μ D = 0.c. Explain how the size of the sample mean difference influences the likelihood of finding a significant mean difference.

Expert Solution

a.

To determine
Sample came from a population with μD=0.

### Explanation of Solution

Given info:

Numbers of participants in the sample are n=9. Mean difference is MD=3.

Sample standard deviation is s=6. Level of significance for two tailed test is α=0.05.

Calculation:

Null Hypothesis: Sample came from a population with μD=0.

Alternate Hypothesis: Sample came from a population with μD0

In repeated-measures study, t statistic under null hypothesis is given by:

t=MDμDsn=3069=1

Expert Solution

b.

To determine
Sample came from a population with μD=0.

Expert Solution

c.

To determine

To explain: How the size of the sample mean difference influences the likelihood of finding a significant mean difference.

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