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 Sham mu mu 1 mu 2 n 12 12 x overbar 0.55 0.45 s 0.83 1.41 a. 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? A. Upper H 0​: mu 1equalsmu 2 Upper H 1​: mu 1not equalsmu 2 B. Upper H 0​: mu 1equalsmu 2 Upper H 1​: mu 1greater thanmu 2 C. Upper H 0​: mu 1less thanmu 2 Upper H 1​: mu 1greater than or equalsmu 2 D. Upper H 0​: mu 1not equalsmu 2 Upper H 1​: mu 1less thanmu 2 The test​ statistic, t, is nothing. ​(Round to two decimal places as​ needed.) The​ P-value is nothing. ​(Round to three decimal places as​ needed.) State the conclusion for the test. ▼ Fail to reject Reject the null hypothesis. There ▼ is 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. Is it valid to argue that magnets might appear to be effective if the sample sizes are​ larger? Since the ▼ sample standard deviation sample mean for those treated with magnets is ▼ greater than equal to less than the sample mean for those given a sham​ treatment, it ▼ is not is 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. nothingless thanmu 1 minus mu 2less than nothing ​(Round to three decimal places as​ needed.)

Answer 1