Question

A research company would like to determine the effectiveness of a pain-relief ointment designed for lower back pain. Prior to testing the ointment, each of the patients fill out a survey to rate their current level of back pain on a scale from 1 to 10. Then, they apply the ointment and after 90 minutes of the application, they fill out the survey a second time. The data are show in the table. If a two-tailed related samples t statistic at the .05 level of significance is computed, what is the value of the variance of the difference (s²_D)? Enter the numerical value below. Include one digit after the decimal point.

Before	After
6	2
8	3
9	4
8	1
10	2
5	3
9	8
7	7

Answer 1

Before	After	Difference	d²
6	2	4	16
8	3	5	25
9	4	5	25
8	1	7	49
10	2	8	64
5	3	2	4
9	8	1	1
7	7	0	0

∑d = 32

∑d² = 184

n = 8

Mean , x̅d = Ʃd/n = 32/8 = 4

Variance of the difference, s²_d = (Ʃd² - (Ʃd)²/n)/(n-1) = (184-(32)²/8)/(8-1) = 8.0