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. Before 10.3 0.6 10.1 11.4 9.9 7.7 3.6 1.1 After 6.9 2.1 7.6 8.7 8.2 6.9 3.9 2.3 a. Construct a​ 95% confidence interval for the mean of the ​"beforeminus​after" differences. nothingless thanmu Subscript dless than nothing ​(Round to two decimal places as​ needed.) b. Use a 0.05 significance level to test the claim that the sensory measurements are lower after hypnotism. Does it appear that the results are lower after​ hypnotism? A. Yes​, because the null hypothesis is not rejected. B. No​, because the null hypothesis is rejected. C. Yes​, because the null hypothesis is rejected. D. No​, because the null hypothesis is not rejected. c. Does hypnotism appear to be effective in reducing​ pain? A. Yes​, because the confidence interval includes zero and the null hypothesis is not rejected. B. No​, because the confidence interval includes zero and the null hypothesis is not rejected. C. Yes​, because the confidence interval does not include zero and the null hypothesis is rejected. D. No​, because the confidence interval does not include zero and the null hypothesis is rejected.

Answer 1

The statistical software output for this problem is:

Paired T confidence interval: μD-HI-u2 : Mean of the difference between Before and After 95% confidence interval results: Difference Mean Std. Er. DF L. Limit U. Limit Before - After 1.0125 0.65749457 7 -0.54222757 2.5672276

Hence,

a) 95% confidence interval:

-0.54 < $\mu_d$ < 2.57

b) No​, because the null hypothesis is not rejected.

c) No​, because the confidence interval includes zero and the null hypothesis is not rejected.