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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 = 30, x=0.58, s = 0.88 Reduction in Pain Level After Sham Treatment (μ₂): n = 30, x = 0.48, s = 1.51 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? A. Ho: M₁

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 = 30, x=0.58, s = 0.88 Reduction in Pain Level After Sham Treatment (μ₂): n = 30, x = 0.48, s = 1.51 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? A. Ho: M₁

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
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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 = 30, x=0.58, s = 0.88 Reduction in Pain Level After Sham Treatment (µ₂): n = 30, x = 0.48, s = 1.51 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? A. Ho: M₁ <H₂ H₁ H₁ H₂ C. Ho: M₁ = ₂ H₁ H₁ H₂ The test statistic, t, is B. Ho: H₁ H₂ H₁: M₁ <H₂ D. Ho: M₁ = ₂ H₁ = µ₁ ‡µ₂ (Round to two decimal places as needed.)
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 = 30, x=0.58, s = 0.88 Reduction in Pain Level After Sham Treatment (µ₂): n = 30, x = 0.48, s = 1.51 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? A. Ho: M₁ <H₂ H₁ H₁ H₂ C. Ho: M₁ = ₂ H₁ H₁ H₂ The test statistic, t, is B. Ho: H₁ H₂ H₁: M₁ <H₂ D. Ho: M₁ = ₂ H₁ = µ₁ ‡µ₂ (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 ▼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). <44-4₂ (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. OA. It appears that magnets are not effective in treating back pain, because 0 is in the confidence interval. OB. It appears that magnets are effective in treating back pain, because the P-value is greater than the significance level. OC. It appears that magnets are not effective in treating back pain, because the P-value is less than the significance level. OD. It appears that magnets are effective in treating back pain, because the confidence interval contains only positive values. Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below. OA. Yes, because increasing the sample size will decrease the P-value. OB. No, because the magnets already appear to be effective. OC. No, because increasing the sample size will increase the P-value. O D. Yes, because increasing the sample size will increase the effectiveness.
Transcribed Image Text:The P-value is. (Round to three decimal places as needed.) State the conclusion for the test. 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). <44-4₂ (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. OA. It appears that magnets are not effective in treating back pain, because 0 is in the confidence interval. OB. It appears that magnets are effective in treating back pain, because the P-value is greater than the significance level. OC. It appears that magnets are not effective in treating back pain, because the P-value is less than the significance level. OD. It appears that magnets are effective in treating back pain, because the confidence interval contains only positive values. Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Choose the correct answer below. OA. Yes, because increasing the sample size will decrease the P-value. OB. No, because the magnets already appear to be effective. OC. No, because increasing the sample size will increase the P-value. O D. Yes, because increasing the sample size will increase the effectiveness.
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