In a study designed to test the effectiveness of magnets for treating back pain,
ID: 3204657 • Letter: I
Question
In a study designed to test the effectiveness of magnets for treating back pain, 35 patients were given a 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 11.0 and a standard deviation of 2.1. After being given the sham treatment, the 35 patients had pain scores with a mean of 11.4 and 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 ?
b. Construct the 99% confidence interval estimate of the mean pain score for patients given the sham treatment.
What is the confidence interval estimate of the population mean ?
c. Compare the results. Does the treatment with magnets appear to be effective?
Option A. Since the confidence intervals overlap, it appears that the magnet treatments are no more effective than the sham treatments.
Option B. Since the confidence intervals overlap, it appears that the magnet treatments are less effective than the sham treatments.
Option C. Since the confidence intervals do not overlap, it appears that the magnet treatments are more effective than the sham treatments.
Option D. Since the confidence intervals do not overlap, it appears that the magnet treatments are no more effective than the sham treatments.
Explanation / Answer
a) For magnet treatments, n = 35 patients, mean= 11.0 and standard deviation = 2.1.
For a 99% confidence interval with 34 degrees of freedom, t = 2 .72
SE = Std. deviation / sqrt( n) = 2.1 / sqrt(35) = 0.354
Confidence interval for mean is = mean + / - t * SE
= 11 + / - 2.72 * 0.354
= (10.034 , 11.965)
b)
For sham treatment, n = 35 patients mean = 11.4 and standard deviation = 2.4
For a 99% confidence interval with 34 degrees of freedom, t = 2 .72
SE = Std. deviation / sqrt( n) = 2.4 / sqrt(35) = 0.405
Confidence interval for mean is = mean + / - t * SE
= 11.4 + / - 2.72 * 0.405
= (10.296 , 12.503)
c) Option D)
Option D. Since the confidence intervals do not overlap, it appears that the magnet treatments are no more effective than the sham treatments.