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

​"beforeminus−​after"

differences. Does hypnotism appear to be effective in reducing​ pain?

Before	4.9	1.9	10.9	12.1	12.4	10.7	7.6	5.4
After	6.6	2.4	7.3	8.4	8.1	6.9	3.8	2.8

Construct a​ 95% confidence interval for the mean of the

Answer 1

95% Confidence interval for mean is given as :

Upper limit :

Lower limit :

Now,

Before	After	(Before-After)
4.9	6.6	-1.7
1.9	2.4	-0.5
10.9	7.3	3.6
12.1	8.4	3.7
12.4	8.1	4.3
10.7	6.9	3.8
7.6	3.8	3.8
5.4	2.8	2.6
Total		19.6

Hence,  

95% Confidence interval for mean is given as :

Upper limit :

Lower limit :