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For a repeated-measures study with n – 12 scores in each treatment, a researcher constructs an 80% confidence interval to describe the mean difference between treatments. What value is at the center of the interval and what t values are used to construct the interval? a. The sample mean difference is at the center and t = ± 1.363. b. The sample mean difference is at the center and t = ± 1.316. c. Zero is at the center and t = ± 1.363. d. Zero is at the center and t = ± 1.316.

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Essentials of Statistics for The B...

9th Edition
Frederick J Gravetter + 2 others
Publisher: Cengage Learning
ISBN: 9781337098120

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for The B...

9th Edition
Frederick J Gravetter + 2 others
Publisher: Cengage Learning
ISBN: 9781337098120
Chapter 11.4, Problem 2LC
Textbook Problem
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For a repeated-measures study with n – 12 scores in each treatment, a researcher constructs an 80% confidence interval to describe the mean difference between treatments. What value is at the center of the interval and what t values are used to construct the interval?

a. The sample mean difference is at the center and t = ± 1.363.

b. The sample mean difference is at the center and t = ± 1.316.

c. Zero is at the center and t = ± 1.363.

d. Zero is at the center and t = ± 1.316.

To determine

To Find: The value at the centre of the interval.

The t values used to construct the interval.

Explanation of Solution

Given info:

Numbers of scores in each treatment are n=12 .

80% confidence interval is given.

Reason for correct answer:

Calculation:

Let n be the numbers of participants in the treatment. Then,

n=12

80% confidence interval is given which means two tailed level of significance is 20%.

Let μD , sMD , t, and MD be the population mean difference, standard error of sample mean difference, critical values and sample mean difference of given two tailed test.

Then, 80% confidence limits are given by the formulae:

μD=MD±t×sMDWhere t is the upper 20% critical values with  (n1)degree of freedom.

Therefore, sample mean difference is at the centre of the confidence interval

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