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)...

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

What are the null and alternative​ hypotheses?

What is the test​ statistic, t?

What is the​ P-value?

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.