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.

	treatment	sham
m	m1	m2
n	29	29
x	.54	.43
s	.85	1.08

a. Use a 0.05 significance​ level, and test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

1. What are the null and alternative​ hypotheses?

2. The test​ statistic,is ______

​(Round to two decimal places as​ needed.)

3. The​ P-value is ______

​(Round to three decimal places as​ needed.)

4. State the conclusion for the test.

________________ the null hypothesis. There ______ sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

5. Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger?

Since the ___________ for those treated with magnets is _________ the sample mean for those given a sham​ treatment, it ___________ valid to argue that magnets might appear to be effective if the sample sizes are larger.

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