# In a study designed to test the effectiveness of magnets for treating

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​ (no pain) to 100​ (extreme pain). After given the magnet​ treatments, the 40 patients had pain scores with a mean of 5.0 and a standard deviation of 2.6. After being given the sham​ treatments, the 40 patients had pain scores with a mean of 4.7and a standard deviation of 2.1. Complete parts​ (a) through​ (c) below.

a. Construct the 90​% confidence interval estimate of the mean pain score for patients given the magnet treatment.

What is the confidence interval estimate of the population mean?

​(Round to one decimal place as​ needed.)

b. Construct the 90% confidence interval estimate of the mean pain score for patients given the sham treatment.

What is the confidence interval estimate of the population mean?

​(Round to one decimal place as​ needed.)

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