Question

In a study designed to test the effectiveness of magnets for treating back​ pain, 40 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 6.0 and a standard deviation of 2.2. After being given the sham​ treatments, the 40 patients had pain scores with a mean of 7.9 and a standard deviation of 2.7. Complete parts​ (a) through​ (c) below.

a. Construct the 90​% confidence interval estimate of the mean pain score for patients given the magnet treatment.

What is the confidence interval estimate of the population mean μ​?

(blank) < μ < (blank) ​(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 μ​?

(blank) < μ < (blank) ​(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 overlap, it appears that the magnet treatments are more effective than the sham treatments.

B.Since the confidence intervals ​overlap, it appears that the magnet treatments are less effective than the sham treatments.

C.Since the confidence intervals do not ​overlap, it appears that the magnet treatments are less effective than the sham treatments.

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

Answer 1

a.

Standard error of sample mean = s / $\sqrt{n}$ = 2.2 / = 0.3478505

V40

Degree of freedom, df = 40 - 1 = 39

Critical value of t at df = 39 and 90% confidence interval is 1.685

Margin of error = t * Standard error = 1.685 * 0.3478505 = 0.586

90% confidence interval is,

(6 - 0.586, 6 + 0.586)

(5.4, 6.6)

5.4 < μ < 6.6

b.

Standard error of sample mean = s / $\sqrt{n}$ = 2.7 / = 0.4269075

V40

Degree of freedom, df = 40 - 1 = 39

Critical value of t at df = 39 and 90% confidence interval is 1.685

Margin of error = t * Standard error = 1.685 * 0.4269075 = 0.719

90% confidence interval is,

(7.9 - 0.719, 7.9 + 0.719)

(7.2, 8.6)

7.2 < μ < 8.6

c.

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