In a study designed to test the effectiveness of magnets for...

In a study designed to test the effectiveness of magnets for treating back​ pain, 35 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 35 patients had pain scores with a mean of 7.0 and a standard deviation of 2.3. After being given the sham​ treatments, the 35 patients had pain scores with a mean of 5.2 and a standard deviation of 2.6. Complete parts​ (a) through​ (c) below.

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

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

First calculate​ E, rounding to three decimal places.