Ina study designed to test the effectiveness magnets for treating back pain, 35 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a

Question

scale from 0(no pain) to 100(extreme pain)
after the given magnet treatments, the 35 patients had pain scores with a mean of 10.0 and a standard deviation of 2.3.
After being given the sham treatments, the 35 patients had pain scores with a mean of 11.8 and a standard deviation of 2.5. What is the confidence interval
estimate of the population mean u? Round to one decimal place as needed. 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
u? c) compare the results. Does the treatment with magnets appear to be effective.

Answer 1

t = 1.697
E = 1.697 *2.3 /√35
E = 0.6597
x -E <μ < x bar + E
10- 0.66< μ < 10 + 0.66
9.34 <μ < 10.66
b.
t = 1.697
E = 1.697* 2.5/√35
E = .7171
x bar-E <μ< x bar+E
11.8 -0.72 <μ < 11.8+ 0.72

11.09 < μ < 12.52

c. Since the confidence intervals not overlap, it appears that the magnet treatments are more effective than the sham treatments.

Answer 2

Assume that a test is given to a large number of people but we do not yet know their scores or the shape of the score distribution. Can we be sure that the sampling distribution of the mean for this test will be normally distributed? Why or why not?
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