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

Before : 9.9 3.3 6.6 9.7 8.5 9.4 5.3 0.6

After: 6.2 2.4 7.2 8.3 8.8 6.6 3.2 2.2

Construct a​ 95% confidence interval for the mean of the "before - after" differences.

Thank you in advance.

Answer 1

sample mean, xbar = 1.05
sample standard deviation, s = 1.8087
sample size, n = 8
degrees of freedom, df = n - 1 = 7

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.36

ME = tc * s/sqrt(n)
ME = 2.36 * 1.8087/sqrt(8)
ME = 1.509

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1.05 - 2.36 * 1.8087/sqrt(8) , 1.05 + 2.36 * 1.8087/sqrt(8))
CI = (-0.46 , 2.56)