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. Treatment Sham μ μ1 μ2 n 29 29 _ x 0.49 0.36 s 0.65 1.31 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. 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 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. __________ ( A. Fail to reject, B. Reject ) the null hypothesis. There __________ ( A. is not, B. 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 _________ ( A. sample mean, B. sample standard deviation ) for those treated with magnets is _______________ ( A. greater than, B. less than C. equal to) the sample mean for those given a sham treatment, it _________ ( A. is, B. is not ) 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.)
Section 9.2
Question #5
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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
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Treatment
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Sham
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μ
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μ1
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μ2
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n
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29
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29
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_ x
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0.49
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0.36
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s
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0.65
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1.31
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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. 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
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.
__________ ( A. Fail to reject, B. Reject ) the null hypothesis. There __________ ( A. is not, B. 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 _________ ( A. sample mean, B. sample standard deviation ) for those treated with magnets is _______________ ( A. greater than, B. less than C. equal to) the sample mean for those given a sham treatment, it
_________ ( A. is, B. is not ) 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.)
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