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 10.0 10.0 and a standard deviation of 2.2. After being given the sham​ treatments, the 40 patients had pain scores with a mean of 9.7and a standard deviation of 2.4. Complete parts​ (a) through​ (c) below. a. Construct the 99% confidence interval estimate of the mean pain score for patients given the magnet treatment. What is the confidence interval estimate of the population mean mu μ​? nothing less than < mu μ less than < nothing ​(Round to one decimal place as​ needed.) b. Construct the 99​% confidence interval estimate of the mean pain score for patients given the sham treatment. What is the confidence interval estimate of the population mean mu μ​? nothing less than < mu μ less than < nothing ​(Round to one decimal place as​ needed.) c. Compare the results. Does the treatment with magnets appear to be​ effective? A. Since the confidence intervals nbsp do not nbsp do not ​overlap, it appears that the magnet treatments are more more effective than the sham treatments. B. Since the confidence intervals nbsp do not nbsp do not ​overlap, it appears that the magnet treatments are no more no more effective than the sham treatments. C. Since the confidence intervals nbsp ​overlap, it appears that the magnet treatments are less less effective than the sham treatments. D. Since the confidence intervals nbsp ​overlap, it appears that the magnet treatments are no more no more effective than the sham treatments.

Answer 1

a) For magnet treatment

DF = 40 - 1 = 39

With 39 degrees of freedom and 99% confidence interval the critical value is t_{0.005, 39} = 2.7079

The confidence interval is

$\bar x$ +/- t_{0.005, 39} *s/sqrt(n)

= 10 +/- 2.7079 * 2/sqrt(40)

= 10 +/- 0.856

= 9.1, 10.9

The confidence interval is 9.1 < $\mu$ < 10.9

b) For sham treatment

The confidence interval is

$\bar x$ +/- t_{0.005, 39} * s/sqrt(n)

= 9.7 +/- 2.7079 * 2.4/sqrt(40)

= 9.7 +/- 1.03

= 8.7, 10.73

c) Option - C