In a study designed to test the effectiveness of magnets for treating back? pain
ID: 3370991 • Letter: I
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 4.0 and a standard deviation of 2.3. After being given the sham? treatments, the 40 patients had pain scores with a mean of 5.9 and a standard deviation of 2.8. Complete parts? (a) through? (c) below. a. Construct the 95?% 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?? nothingless thanmuless than nothing ?(Round to one decimal place as? needed.) b. Construct the 95?% confidence interval estimate of the mean pain score for patients given the sham treatment. What is the confidence interval estimate of the population mean mu?? nothingless thanmuless than nothing ?(Round to one decimal place as? needed.) c. Compare the results. Does the treatment with magnets appear to be? effective?
Explanation / Answer
a)
z value at 95% = 1.96
CI = mean +/- z *(s/sqrt(n))
= 4 +/- 1.96 *(2.3/sqrt(40))
= (3.2872,4.7128)
3.3 < mu < 4.7
b)
z value at 95% = 1.96
CI = mean +/- z *(s/sqrt(n))
= 5.9 +/- 1.96 *(2.8/sqrt(40))
= (5.0323,6.7677)
5 < mu < 6.8
c)
No