In a study designed to test the effectiveness of magnets for treating back pain, 20 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a standard Visual Analog Scale (VAS). After given the magnet treatments, the 20 patients had VAS scores with a mean of 5.0 and a standard deviation of 2.4. After being given the sham treatments, the 20 patients had VAS scores with a mean of 4.7 and a standard deviation of 2.9.

a. Construct the 95% confidence interval estimate of the mean VAS score for patients given the magnet treatment.

b. Construct the 95% confidence interval estimate of the mean VAS score for patients given a sham treatment.

c. Compare the results. Does the treatment with magnets appear to be effective?