In a study designed to test the effectiveness of magnets for treating back pain,
ID: 2927621 • 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 12.0 and a standard deviation of 2.4. After being given the sham treatments, the 40 patients had pain scores with a mean of 12.4 and a standard deviation of 2.6.
Complete parts (a) through (c) below.
a. What is the confidence interval estimate of the population mean ?
b. Construct the 95% confidence interval edtimate of the mean pain score for patients given the sham treatment.
C. What is the confidence interval population mean ?
Explanation / Answer
a). Construct the 90% confidence interval estimate of the mean pain score for patients given the magnet treatment.
Ans:
z_c = 1.96 at 95% confidence.
n = 40
x-bar = 12
sd = 2.4
margin of error, E = (sd*z_c)/sqrt(n) = (2.4*1.96)/sqrt(40) = 0.744
95% Confidence Interval = (x-bar - E , x-bar + E)
= (12 - 0.744 , 12 + 0.744)
= (11.256, 12.744)
b). Construct the 95% confidence interval estimate of the mean pain score for patients given the sham treatment.
z_c = 1.96 at 95% confidence.
n = 40
x-bar = 12.4
sd = 2.6
margin of error, E = (sd*z_c)/sqrt(n) = (2.6*1.96)/sqrt(40) = 0.806
95% Confidence Interval = (x-bar - E , x-bar + E)
= (12.4 - 0.806 , 12.4 + 0.806)
= (11.594, 13.206)
c. Does the treatment with magnets appear to be effective?
ANs: Intervals overlap, so treatments are less effective