In a study designed to test the effectiveness of magnets for treating back pain, 40 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale from 0 to 100. After given the magnet treatments, the 40 patients had pain scores with a mean of 9.0 and a standard deviation of 2.3. After being given the sham treatment, the 40 patients had pain scores with a mean of 9.2 and a standard deviation of 2.5. Complete parts (a) through (c) below.

Question

a. Construct the 99% confidence interval estimate of the mean pain score for patients given the magnet treatment. What is the confidence interval of the population mean µ?
?<µ<? Round to one decimal place as needed
b. Construct the 99% confidence interval estimate of the mean pain score for the patients given the sham treatment. What is the confidence interval estimate of the population mean µ?
?<µ<? Round to one decimal place as needed
c. Compare the results. Does the treatment with magnets appear to be effective?

Answer 1

t = 2.75
E = 2.75*2.3/ √40
E = 1.00
xbar -E <μ < x bar + E
9 - < μ < 9 + 1.00
8.00 μ < 10.00
b.
t = 2.75
E = 2.75 * 2.5/√40
E = 1.089
x bar -E<μ x bar +E

9.2- 1.089< μ < 9.2 +1.089

8.111< μ < 10.287

c. Since the confidence intervals overlap, it appears that the magnet treatments are no more effective than the sham treatments.