Question

In: Statistics and Probability

In a study designed to test the effectiveness of magnets for treating back? pain, 35 patients...

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 sham treatment without magnets. Pain was measured using a scale from 0? (no pain) to 100? (extreme pain). After given the magnet? treatments, the 35 patients had pain scores with a mean of 9.0 and a standard deviation of 2.2. After being given the sham? treatments, the 35 patients had pain scores with a mean of 8.6 and a standard deviation of 2.8. Complete parts? (a) through? (c) below.

a. Construct the 95?% 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???

______less than ? less than______

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

b. Construct the 95?% 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???

______less than u less than ______

?(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 no more effective than the sham treatments.

B. Since the confidence intervals ?overlap, it appears that the magnet treatments are more 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.

Solutions

Expert Solution

a. Construct the 95?% confidence interval estimate of the mean pain score for patients given the magnet treatment.

What is the confidence interval estimate of the population mean ?

Answer: We are given:

The 95% confidence interval is given below:

Where is the critical value of t at 0.05 significance level and for 34 degrees of freedom and is given below:

Therefore the 95% confidence interval estimate of the mean pain score for patients given the magnet treatment is

b. Construct the 95?% confidence interval estimate of the mean pain score for patients given the sham treatment.

What is the confidence interval estimate of the population mean ?

Answer: We are given:

The 95% confidence interval is given below:

Where is the critical value of t at 0.05 significance level and for 34 degrees of freedom and is given below:

Therefore the 95% confidence interval estimate of the mean pain score for patients given the magnet treatment is

c. Compare the results. Does the treatment with magnets appear to be? effective?

Answer: A. Since the confidence intervals ?overlap, it appears that the magnet treatments are no more effective than the sham treatments.

orchestra answered 1 year ago

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