Question

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain scale before and after hypnosis. Assume that the paired sample data are simple random samples and that the differences have a distribution that is approximately normal. Construct a​ 95% confidence interval for the mean of the "before minus−​after" differences. Does hypnotism appear to be effective in reducing​ pain?

Before	6.7	2.5	6.8	9.3	12.5	11.2	2.9	2.0
After	6.4	2.2	7.1	8.1	8.6	6.7	3.6	2.5

Answer 1

Solution:

The required confidence interval is given as below:

Confidence interval = Dbar ± t*S_D/sqrt(n)

From given data, we have

Dbar = 1.0875

S_d = 2.0160

n = 8

df = n – 1 = 7

Confidence level = 95%

Critical t value = 2.3646

(by using t-table)

Confidence interval = Dbar ± t*S_D/sqrt(n)

Confidence interval = 1.0875 ± 2.3646*2.0160/sqrt(8)

Confidence interval = 1.0875 ± 2.3646*0.712763635

Confidence interval = 1.0875 ± 1.6854

Lower limit = 1.0875 - 1.6854 = -0.5979

Upper limit = 1.0875 + 1.6854 = 2.7729

Confidence interval = (-0.5979, 2.7729)

Hypnotism does not appear to be effective in reducing pain because above interval contains zero.