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. Test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative​ hypotheses? 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. b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.			Treatment	Sham
		muμ	mu 1μ1	mu 2μ2
		n	12	12
		x overbarx	0.49	0.42
		s	0.74	1.08

Answer 1

Here we will use independent sample t-test to determine whether magnets are effective in treating back pain.

And the procedure is

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the magnets are effective in treating back pain.​, at the 0.05 significance level.

b)

Confidence Interval

The 95% confidence interval is −0.72<μ1​−μ2​<0.86.