Question

A study was conducted to measure the effectiveness of hypnotism in reducing pain.The measurements are centimeters are 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 – after differences. Does hypnotism appear to be effective in reducing pain?

Before 8.5 4.5 8.9. 13.1. 8.0. 7.6. 1.6 0.7

After. 6.2. 2.9. 7.5. 8.5. 8.6. 6.5. 3.4. 2.5

construct a 95 percent comfidence interval for the mean of the "before-after" differences .

Answer 1

Solution:

Confidence interval for average difference of paired samples is given as below:

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

From given data, we have

Before	After	Difference
8.5	6.2	2.3
4.5	2.9	1.6
8.9	7.5	1.4
13.1	8.5	4.6
8	8.6	-0.6
7.6	6.5	1.1
1.6	3.4	-1.8
0.7	2.5	-1.8

Dbar = 0.85

S_d = 2.17912171

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 = 0.85 ± 2.3646*2.17912171/sqrt(8)

Confidence interval = 0.85 ± 1.8218

Lower limit = 0.85 - 1.8218 = -0.97

Upper limit = 0.85 + 1.8218 = 2.67

-0.97 < µ_d < 2.67

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