A researcher would like to evaluate the effectiveness of a pain-relief patch designed for lower back pain. Prior to testing the patch, each of n = 8 patients rates the current level of back pain on a scale from 1 to 10. After wearing the patch for 90 minutes, a second pain rating is recorded. The data are as follows: Include in your responses:K. Use mathematical notation to present the resultsL. Compute Cohen’s d to measure the size of the effect.M. Write a concise conclusion statement that includes the results of the study and the effect size. **Data Table: Before and After Analysis**This table presents a side-by-side comparison of two sets of numerical values, labeled "Before" and "After." It consists of the following entries:- Before: 6, After: 2- Before: 8, After: 3- Before: 9, After: 4- Before: 8, After: 1- Before: 10, After: 2- Before: 5, After: 3- Before: 9, After: 8- Before: 7, After: 7The table shows the transformation or changes between the "Before" and "After" values across eight different instances. Each pair of numbers represents the before and after values for a specific case, illustrating changes or effects due to an intervention, process, or other influencing factors.

Name: A researcher would like to evaluate the effectiveness of a pain-relief
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: A researcher would like to evaluate the effectiveness of a pain-relief patch designed for lower back pain. Prior to testing the patch, each of n = 8 patients rates the current level of back pain on a scale from 1 to 10. After wearing the patch for 90

This is a paired t-test. The task is to test the effectiveness of a pain-relief patch designed for lower back pain. The hypothesis are given as : Ho : μd = 0H1 : μd ≠ 0,μd = μ1-μ2 Let the level of significance be α=0.05, The test statistics is given by Students' T-distribution with n-1 degrees of freedom. t=dSd/n~tn-1 where, d= difference between the data point of two setsSd= standard deviation of the differencesBefore After d 6 2 4 8 3 5 9 4 5 8 1 7 10 2 8 5 3 2 9 8 1 7 7 0 Average 4 S.D 2.828 The test statistics is : t=42.828/8=4.00060 The tabulated t-value with 7 degrees of freedom at α=0.05 (two-tailed) level of significance is 2.365. According to the decision rule, null hypothesis is rejected when calculated test statistics is greater than the tabulated t-value and is accepted otherwise. 4.00060 > 2.365 - Reject Ho Cohen's d is 4/2.828=1.414 Conclusion : The null hypothesis is rejected indicating that there is difference in the pain before and after using the pain relief patch. The Cohen's -d is large, implying larger difference between the average and the true population mean.