In a study designed to test the effectiveness of magnets for treating back pain
ID: 3125810 • Letter: I
Question
In a study designed to test the effectiveness of magnets for treating back pain 35 patients were given a treatment with magnets and also a sharm treatment without magnets. Pain was measured using a scale from to 100 (extreme pain) After given the magnet treatment, 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 a standard deviation of 2.5 complete parts (a) through (c) below.Explanation / Answer
a)
For magnet treatments:
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 11
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 2.1
n = sample size = 35
Thus,
Margin of Error E = 0.9143287
Lower bound = 10.0856713
Upper bound = 11.9143287
Thus, the confidence interval is
( 10.0856713 , 11.9143287 ) [ANSWER]
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b)
For sham treatments:
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 11.4
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 2.5
n = sample size = 35
Thus,
Margin of Error E = 1.088486548
Lower bound = 10.31151345
Upper bound = 12.48848655
Thus, the confidence interval is
( 10.31151345 , 12.48848655 ) [ANSWER]
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c)
OPTION C: Since the confidence intervals overlap, it appears that the magnet treatments are no more effective than the sham treatments. [ANSWER]