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Essentials of Statistics for the B...

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

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Solve the following problems.

a. A repeated-measures study with a sample of n = 16 participants produces a mean difference of MD = 3 with a standard deviation of s = 4. Use a two-tailed hypothesis test with α – .05 to determine whether this sample provides evidence of a significant treatment effect.

b. Now assume that the sample standard deviation is s = 12 and repeat the hypothesis test.

c. Explain how the size of the sample standard deviation influences the likelihood of finding a significant mean difference.

a.

To determine

To check: Whether the sample provides evidence of a significant treatment effect or not.

Explanation

Given info:

Numbers of college participants in the sample are n=16 .

Mean difference is MD=3 .

Sample standard deviation is s=4 .

Level of significance for two tailed test is α=0.05 .

Calculation:

The hypotheses are given below:

Null Hypothesis:

H0:μD=0

That is, there is no difference due to different treatments.

Alternate Hypothesis:

H1:μD0

That is, there is significant difference due to the treatments.

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

t=MDμD

b.

To determine

The sample provides evidence of a significant treatment effect.

c.

To determine

To Explain: How the size of the sample standard deviation influences the likelihood of finding a significant mean difference.

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