Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis H: DD= 0 (the null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.Complete the following table by calculating the differences and the squared differences:

Observation	A	B	Difference Score	Squared Difference Score
(D = B - A)	(D)
1	1	3
2	3	4
3	5	7
4	4	4
5	8	9

The mean difference score is MDD= .

For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and sMDMD.What is the estimated standard deviation of the difference scores?

s

=

/

=

2.80 /

=

What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of s.)

sMDMD

=

s /

=

What is the t statistic for the repeated-measures t test to test the null hypothesis H: DD= 0?

t

=

MDD- /

=

3.21

t Distribution

Degrees of Freedom = 7

-4.0-3.0-2.0-1.00.01.02.03.04.0t.2500.5000.2500-0.7110.711

You conduct a two-tailed test at = .05. To use the Distributions tool to find the critical values, you first need to set the degrees of freedom in the tool. The degrees of freedom are .

The critical values (the values for t scores that separate the tails from the main body of the distribution, forming the critical region) are .

Finally, since the t statistic in the critical region, you the null hypothesis.