In a study designed to test the effectiveness of magnets for treating back pain,
ID: 3073775 • 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 11.0 and a standard deviation of 2.3. After being given the sham treatments, the 40 patients had pain scores with a mean of 10.8 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. What is the confidence interval estimate of the population mean mu?
____ < u<____
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 mu?
____ < u < ____
C. Compare the results. Does the treatment with magnets appear to be effective? And why?
Explanation / Answer
a)
z value at 90% = 1.645
mean = 11 , s = 2.3 , n = 40
CI = mean +/- z *(s/sqrt(n))
= 11 +/- 1.645 *(2.3/sqrt(40))
= (10.4018,11.5982)
10.4018 < mu < 11.5982
b)
z value at 90% = 1.645
mean = 10.8 , s = 2.6 , n = 40
CI = mean +/- z *(s/sqrt(n))
= 10.8 +/- 1.645 *(2.6/sqrt(40))
= (10.1237,11.4763)
10.1237< mu < 11.4763
c)
Treatments with magnets not appear to be effective because difference in interval is less than the sham treatments