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. n 17 17 0.49 0.37 0.96 1.22 a. Use a 0.05 significance level to 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? OA. H H, "H2 O B. Ho H, <2 Elz :'H OD. Ho H "H2 OC. Hgi H "H2 H: H2 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. the null hypothesis. There than those given a sham treatment. sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain In it valid to argue that magnets might appear to be effective if the sample sizes are larger? the sample mean for those given a sham treatment, it valid to argu Since the for those treated with magnets is 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. (Round to three decimal places as needed.)

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If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

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The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.