The inflammation caused by osteoarthritis of the knee can be very painful and can inhibit movement. Leech saliva contains anti-inflammatory substances. To study the therapeutic effect of attaching four to six leeches to the knee for about 70 minutes, 51 volunteers were randomly assigned to receive either the leech treatment or a topical gel, diclofenac. This summary table gives the results of a pretreatment measure of the amount of pain reported by the two groups, before beginning therapy. A higher score means more pain. The researchers hoped that the randomization would result in two comparable groups with respect to this variable. You may assume that the pain scores are approximately normal for each group. Leech (Group 1): x⎯⎯⎯x¯ = 52.4, ss = 13.9, nn = 24 Topical gel (Group 2): x⎯⎯⎯x¯ = 52, ss = 16.6, nn = 27 Unless otherwise stated, give your answers to three decimal places. Construct a 99% confidence interval for the difference in average pain score. Give your answers to two decimal places. Use t∗=2.680t∗=2.680. ( , ) Conduct a hypothesis test to determine whether the average pain score is different for the leech and topical gel groups. What is the parameter of interest? i. pp ii. μμ iii. p1−p2p1−p2 iv. μ1−μ2μ1−μ2 v. μdμd What is the correct null value for this test? What sign should appear in the alternative hypothesis? i. == ii. << iii. >> iv. ≠≠ The test statistic for this test is t=t= . The p-value for this test is . Use df=48.842df=48.842. (If p-value <0.001<0.001, enter 0). Select the appropriate decision for this hypothesis test (use α=0.1α=0.1). i. Reject H0H0 ii. Fail to reject H0H0 iii. Accept H0H0 Select the appropriate interpretation for this hypothesis test (use α=0.1α=0.1). i. We do not have statistically significant evidence to suggest that the average pain score is different for the leech group than the topical gel. ii. We have statistically significant evidence to suggest that the average pain score is different for the leech group than the topical gel. iii. We have statistically significant evidence to suggest that the average pain score is the same for the leech group and the topical gel. If an error had been made on this test, what kind of error would it have been? i. Type I error ii. Type II error

The inflammation caused by osteoarthritis of the knee can be very painful and can inhibit movement. Leech saliva contains anti-inflammatory substances. To study the therapeutic effect of attaching four to six leeches to the knee for about 70 minutes, 51 volunteers were randomly assigned to receive either the leech treatment or a topical gel, diclofenac. This summary table gives the results of a pretreatment measure of the amount of pain reported by the two groups, before beginning therapy. A higher score means more pain. The researchers hoped that the randomization would result in two comparable groups with respect to this variable. You may assume that the pain scores are approximately normal for each group. Leech (Group 1): x⎯⎯⎯x¯ = 52.4, ss = 13.9, nn = 24 Topical gel (Group 2): x⎯⎯⎯x¯ = 52, ss = 16.6, nn = 27 Unless otherwise stated, give your answers to three decimal places. Construct a 99% confidence interval for the difference in average pain score. Give your answers to two decimal places. Use t∗=2.680t∗=2.680. ( , ) Conduct a hypothesis test to determine whether the average pain score is different for the leech and topical gel groups. What is the parameter of interest? i. pp ii. μμ iii. p1−p2p1−p2 iv. μ1−μ2μ1−μ2 v. μdμd What is the correct null value for this test? What sign should appear in the alternative hypothesis? i. == ii. << iii. >> iv. ≠≠ The test statistic for this test is t=t= . The p-value for this test is . Use df=48.842df=48.842. (If p-value <0.001<0.001, enter 0). Select the appropriate decision for this hypothesis test (use α=0.1α=0.1). i. Reject H0H0 ii. Fail to reject H0H0 iii. Accept H0H0 Select the appropriate interpretation for this hypothesis test (use α=0.1α=0.1). i. We do not have statistically significant evidence to suggest that the average pain score is different for the leech group than the topical gel. ii. We have statistically significant evidence to suggest that the average pain score is different for the leech group than the topical gel. iii. We have statistically significant evidence to suggest that the average pain score is the same for the leech group and the topical gel. If an error had been made on this test, what kind of error would it have been? i. Type I error ii. Type II error

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

This summary table gives the results of a pretreatment measure of the amount of pain reported by the two groups, before beginning therapy. A higher score means more pain. The researchers hoped that the randomization would result in two comparable groups with respect to this variable.

You may assume that the pain scores are approximately normal for each group.

Leech (Group 1): x⎯⎯⎯x¯ = 52.4, ss = 13.9, nn = 24
Topical gel (Group 2): x⎯⎯⎯x¯ = 52, ss = 16.6, nn = 27

Unless otherwise stated, give your answers to three decimal places.

Construct a 99% confidence interval for the difference in average pain score. Give your answers to two decimal places. Use t∗=2.680t∗=2.680.
( , )
Conduct a hypothesis test to determine whether the average pain score is different for the leech and topical gel groups.
1. What is the parameter of interest?
  i. pp
  ii. μμ
  iii. p1−p2p1−p2
  iv. μ1−μ2μ1−μ2
  v. μdμd
2. What is the correct null value for this test?
3. What sign should appear in the alternative hypothesis?
  i. == ii. << iii. >> iv. ≠≠
4. The test statistic for this test is t=t= .
5. The p-value for this test is . Use df=48.842df=48.842. (If p-value <0.001<0.001, enter 0).
6. Select the appropriate decision for this hypothesis test (use α=0.1α=0.1).
  i. Reject H0H0 ii. Fail to reject H0H0 iii. Accept H0H0
7. Select the appropriate interpretation for this hypothesis test (use α=0.1α=0.1).
  i. We do not have statistically significant evidence to suggest that the average pain score is different for the leech group than the topical gel.
  ii. We have statistically significant evidence to suggest that the average pain score is different for the leech group than the topical gel.
  iii. We have statistically significant evidence to suggest that the average pain score is the same for the leech group and the topical gel.
8. If an error had been made on this test, what kind of error would it have been?
  i. Type I error ii. Type II error

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