   # A sample of difference scores from a repeated-measures experiment has a mean of M d = 3 with a standard deviation of s = 4 . a. If n = 4 , is this sample sufficient to reject the null hypothesis using a two-tailed test with α = .05 ? b. Would you reject H 0 if n = 16 ? Again, assume a two-tailed test with α = .05 . c. Explain how the size of the sample influences the likelihood of finding a significant mean difference. ### Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781305504912

#### Solutions

Chapter
Section ### Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781305504912
Chapter 11, Problem 19P
Textbook Problem
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## A sample of difference scores from a repeated-measures experiment has a mean of M d = 3 with a standard deviation of s = 4 . a. If n = 4 , is this sample sufficient to reject the null hypothesis using a two-tailed test with α = .05 ? b. Would you reject H 0 if n = 16 ? Again, assume a two-tailed test with α = .05 . c. Explain how the size of the sample influences the likelihood of finding a significant mean difference.

To determine

Do these data indicate a significant mean difference. How the size of the sample influences the likelihood of finding a significant mean difference.

### Explanation of Solution

We are given to use a two-tailed test. That's why alternative hypothesis has sign.

1. The critical value of t values for the critical region are t=±3.182 . So, reject null hypothesis if t<3.182 or t>3.182 .
2. The critical value of t values for the critical region are t=±2.131 . So, reject null hypothesis if t<2.131 or t>2.131 .

Given:

1. M D =3 , n=4 , S D =4 and α=0.05 .
2. M D =3 , n=16 , S D =4 and α=0.05 .1

Formula used:

df=n1 t= M D μ D S D / n

Calculation:

1. When n=4 :

STEP 1: State the hypotheses. The null hypothesis states that there is no significant mean difference. In symbols:

H 0 : μ D =0

The alternative hypothesis states that there is significant mean difference. In symbols:

H a : μ D 0

STEP 2: Locate the critical region. Degree of freedom is:

df=n1 =41 =3 From the t distribution table, for a two-tailed test with α=0.05 for df=3 , the critical value of t values for the critical region are t=±3.182 .

STEP 3: Compute the test statistic. The test statistic is:

t= M D μ D S D / n = 30 4/ 4 =1

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