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. 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? A. $H_0: \mu_1 \neq \mu_2$ $H_1: \mu_1 < \mu_2$ C. $H_0: \mu_1 = \mu_2$ $H_1: \mu_1 > \mu_2$ B. $H_0: \mu_1 \leq \mu_2$ $H_1: \mu_1 \geq \mu_2$ D. $H_0: \mu_1 = \mu_2$ $H_1: \mu_1 \neq \mu_2$ Treatment Sham $\mu$ $\mu_1$ $\mu_2$ n 13 13 x 0.48 0.46 s 0.62 1.48
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The null hypothesis (Ho) states that there is no difference in the mean reduction in pain between those treated with magnets and those given a sham treatment. In other words, the mean reduction in pain for both groups is equal or the mean reduction in pain for Show more…
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State the conclusion for the test. The null hypothesis. There is 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 for those treated with magnets is the sample mean for those given a sham treatment, it is valid to argue that magnets might appear to be effective if the sample sizes are larger.
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Assume a significance level of ? = 0.05 and use the given information for the following: a. State a conclusion about the null hypothesis. (Reject H 0 or fail to reject H 0 . ) b. Without using technical terms, state a final conclusion that addresses the original claim. Original claim: The percentage of blue M&Ms is greater than 5%. The hypothesis test results in a P-value of 0.0010.
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