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	9.79.7	6.36.3	8.98.9	9.49.4	11.011.0	11.711.7	5.45.4	6.56.5
After	6.36.3	2.62.6	7.47.4	8.58.5	8.78.7	6.96.9	3.33.3	2.8

Answer 1

The Calculation table for mean and standard deviation

Before	After	d =before-after	d^2
9.7	6.3	3.4	11.56
6.3	2.6	3.7	13.69
8.9	7.4	1.5	2.25
9.4	8.5	0.9	0.81
11	8.7	2.3	5.29
11.7	6.9	4.8	23.04
5.4	3.3	2.1	4.41
6.5	2.8	3.7	13.69
	Total	22.4	74.74

Degrees of freedom = n-1= 8-1 = 7

The critical value of t for 7 df with 95% Confidence is 2.365

95% CI for the mean of differences is

The 95% CI is ( 1.704, 3.896)

Conclusion : Since both the limits of confidence interval is positive and does not include zero, that means the pain scale before hypnosis is greater than after hypnosis. Hence hypnotism appear to be effective in reducing​ pain.