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Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (₁): n=24, x=0.56, s=1.04 Reduction in Pain Level After Sham Treatment (p₂): n=24, x=0.49, s= 1.56 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 (similar to a placebo). What are the null and alternative hypotheses? OA H₂: H₁ = 1/2 H₂H4₂ OC. H₂: H₁ = 4/2 H₂: Hy #1₂ The test statistic, t, is. (Round to two decimal places as needed.) The P-value is. (Round to three decimal places needed.) State the conclusion for the test. OB. Ho: P₁ P₂ H₁ H₁ H₂ the null hypothesis. There b. Construct a confidence interval appropriate for the hypothesis test in part (a).

Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (₁): n=24, x=0.56, s=1.04 Reduction in Pain Level After Sham Treatment (p₂): n=24, x=0.49, s= 1.56 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 (similar to a placebo). What are the null and alternative hypotheses? OA H₂: H₁ = 1/2 H₂H4₂ OC. H₂: H₁ = 4/2 H₂: Hy #1₂ The test statistic, t, is. (Round to two decimal places as needed.) The P-value is. (Round to three decimal places needed.) State the conclusion for the test. OB. Ho: P₁ P₂ H₁ H₁ H₂ the null hypothesis. There b. Construct a confidence interval appropriate for the hypothesis test in part (a).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (µ₁): n = 24, x = 0.56, s = 1.04 Reduction in Pain Level After Sham Treatment (µ₂): n = 24, x = 0.49, s = 1.56 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 (similar to a placebo). What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: M1 = µ¹₂ H₁: H₁ H₂ (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) The test statistic, t, is State the conclusion for the test. B. Ho: H₁ H2 H₁: M₁ <H₂ the null hypothesis. There sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. b. Construct a confidence interval appropriate for the hypothesis test in part (a). A. It appears that magnets are not effective in treating back pain, because 0 is in the confidence interval. B. It appears that magnets are effective in treating back pain, because the confidence interval contains only positive values. C. It appears that magnets are not effective in treating back pain, because the P-value is less than the significance level. D. It appears that magnets are effective in treating back pain, because the P-value is greater than the significance level. Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below. OD. Ho: H1 H₂ H₁: H₁ H₂ <H₁-H₂< (Round to two decimal places as needed.) c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below. A. No, because the magnets already appear to be effective. B. No, because increasing the sample size will increase the P-value. C. Yes, because increasing the sample size will decrease the P-value. D. Yes, because increasing the sample size will increase the effectiveness.
Transcribed Image Text:Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. 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) to (c) below. Reduction in Pain Level After Magnet Treatment (µ₁): n = 24, x = 0.56, s = 1.04 Reduction in Pain Level After Sham Treatment (µ₂): n = 24, x = 0.49, s = 1.56 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 (similar to a placebo). What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: M1 = µ¹₂ H₁: H₁ H₂ (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) The test statistic, t, is State the conclusion for the test. B. Ho: H₁ H2 H₁: M₁ <H₂ the null hypothesis. There sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. b. Construct a confidence interval appropriate for the hypothesis test in part (a). A. It appears that magnets are not effective in treating back pain, because 0 is in the confidence interval. B. It appears that magnets are effective in treating back pain, because the confidence interval contains only positive values. C. It appears that magnets are not effective in treating back pain, because the P-value is less than the significance level. D. It appears that magnets are effective in treating back pain, because the P-value is greater than the significance level. Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below. OD. Ho: H1 H₂ H₁: H₁ H₂ <H₁-H₂< (Round to two decimal places as needed.) c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below. A. No, because the magnets already appear to be effective. B. No, because increasing the sample size will increase the P-value. C. Yes, because increasing the sample size will decrease the P-value. D. Yes, because increasing the sample size will increase the effectiveness.
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