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 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? 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 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.)			Treatment	Sham
		μ	μ1	μ2
		n	21	21
		x	0.57	0.43
		s	0.77	1.17

Answer 1

using minitab>stat>basic stat>two sample t

we have

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 21 0.6 77.0 17
2 21 0.43 1.17 0.26

Difference = μ (1) - μ (2)
Estimate for difference: 0.1
95% CI for difference: (-34.9, 35.2)
T-Test of difference = 0 (vs >): T-Value = 0.01 P-Value = 0.497 DF = 20
Ans 1 ) the null and alternate hypothesis is given by option C

C. H0​: μ1 = μ2

H1​: μ1 > μ2

Ans 2 ) the test stst is 0.01

Ans 3 ) p value is 0.497

Ans 4 ) Do not reject the null hypothesis. There is not sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

Ans 5 ) Since the sample mean  for those treated with magnets is different the sample mean for those given sham​ treatment, it is valid to argue that magnets might appear to be effective if the sample sizes are larger.

Ans 6 ) from output we have

-34.899 < μ1−μ2 < 35.199