Question

In a study designed to test the effectiveness of magnets for treating back​ pain,

4040

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

4040

patients had pain scores with a mean of

11.011.0

and a standard deviation of

2.72.7.

After being given the sham​ treatments, the

4040

patients had pain scores with a mean of

9.29.2

and a standard deviation of

2.42.4.

Complete parts​ (a) through​ (c) below.Click here to view a t distribution table.

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Click here to view page 1 of the standard normal distribution table.

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Click here to view page 2 of the standard normal distribution table.

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a. Construct the

9595​%

confidence interval estimate of the mean pain score for patients given the magnet treatment.What is the confidence interval estimate of the population mean

muμ​?

nothingless than<muμless than<nothing

​(Round to one decimal place as​ needed.)

Answer 1

With Magnet:

N    Mean StDev SE Mean       95% CI
40 11.000 2.700    0.427     (10.136, 11.864)

95​% confidence interval estimate of the mean pain score for patients given the magnet treatment: (10.1, 11.9)

Without Magnet:

One-Sample T

N   Mean StDev SE Mean      95% CI
40 9.200 2.400    0.379    (8.432, 9.968)

95​% confidence interval estimate of the mean pain score for patients without given the magnet treatment: (8.4, 10.1).

Note: We see from 95% C.I. s that the upper limit of 95​% confidence interval estimate of the mean pain score for patients without given the magnet treatment is less than the lower limit of 95​% confidence interval estimate of the mean pain score for patients given the magnet treatment. Hence we 95% confident that magnets for treating back​ pain is more effective than treating back pain without magnet.