In a study designed to test the effectiveness of magnets for treating back pain,
ID: 3222376 • Letter: I
Question
In a study designed to test the effectiveness of magnets for treating back pain, 40 patients were given a treatement 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 give the sham treatments, the 40 patients had pain scores with a mean of 4.3 and a standard deviation of 2.2 .
a. Construct the 90% confidence interval estimate of the mean pain score for patienst given the magnet treatment.
What is the confidence interval estimate of the populaition mean ?
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b. Construct the 90% confidence interval estimate of the mean pain score for patients givent the sham treatment.
What is the confidence interval estimate of the population mean ?
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c. Compair the results. Does the treatment with magnets appear to be effective?
Please show how the process of solving the answer step by step.
Explanation / Answer
GIVEN
FOR Sham treatment
x- Sample mean = 6.0
s: Sample standard deviation = 2.6
n: Number of samples = 40
df: degrees of freedom =N-1=40-1= 39
standard error ; s/n=2.6/40=0.4110
margin of error = critical value * standard error=1.645*04110=0.6760
for magnet treatment
x-bar: Sample mean = 4.3
s: Sample standard deviation = 2.2
n: Number of samples = 40
df: degrees of freedom =N-1=40-1= 39
standard error ; s/n=2.2/40=0.3478
margin of error = critical value * standard error=1.645*0.3478 = 0.5721
90% c.i z score from standard z table = 1.645
we know confidence interval formulea estimation of population mean is given by
x -M.E < < x bar + ME
A) 6- 0.6760< < 6 + 0.6760
5.324 < <6.676
B) x -M.E < < x bar + ME
4.3- 0.5721 < < 4.3+0.5721
3.7279 < < 4.8721
C) Since the confidence intervals do not overlap, it appears that the magnet treatments are no more effective than the sham treatments.
C)