Question

Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment​ (with magnets) group and the sham​ (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.05 significance level for both parts

    Treatment                Placebo

μ          μ1                    μ2

n          21                    21

x          0.49                 0.44

s           0.64                 1.43

a. Test the claim that the two samples are from populations with the same mean.

What are the null and alternative​ hypotheses?

A. H0​: μ1<μ2

H1​: μ1≥μ2

B. H0​: μ1=μ2

H1​: μ1>μ2

C. H0​: μ1=μ2

H1​: μ1≠μ2

D. H0​: μ1≠μ2

H1​: μ1<μ2

The test​ statistic, t, is _____. ​(Round to two decimal places as​ needed.)

The​ P-value is _____. ​(Round to three decimal places as​ needed.)

State the conclusion for the test.

(1)_____ the null hypothesis. There (2)_____ sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger? Since the (3)_____ for those treated with magnets is (4) _____ the sample mean for those given a sham​ treatment, it (5)_____ valid to argue that magnets might appear to be effective if the sample sizes are larger.

(1) Reject

Fail to reject

(2) is not

is

(3) sample mean

sample standard deviation

(4) less than

greater than

equal to

(5) is not

is

b. Construct a confidence interval suitable for testing the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

_____<μ1−μ2<_____ ​(Round to three decimal places as​ needed.)

Answer 1