Question

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 6.0 and a standard deviation of 2.6. After being given the sham​ treatments, the 40 patients had pain scores with a mean of 5.8 and a standard deviation of 2.4. Complete parts​ (a) through​ (c) below.

a. Construct the 99​% confidence interval estimate of the mean pain score for patients given the magnet treatment.
What is the confidence interval estimate of the population mean mu​?

(b)

Answer 1

a)

t critical value at 0.01 significance level with 39 df = 2.708

99% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

6 - 2.708 * 2.6 / sqrt(40) < < 6 + 2.708 * 2.6 / sqrt(40)

4.89 < < 7.11

99% CI is ( 4.89 , 7.11 )