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:D. Calculate S2DE. Calculate S2 for the sampling distribution of Mean differencesF. Calculate Standard error ### Data Comparison: Before and AfterThe table below presents a set of values categorized under two columns: "Before" and "After." This data can be used to analyze changes or effects between two conditions. | Before | After ||--------|-------|| 6 | 2 || 8 | 3 || 9 | 4 || 8 | 1 || 10 | 2 || 5 | 3 || 9 | 8 || 7 | 7 |### Analysis- **Decrement Pattern**: Several "After" values show a noticeable decrease compared to their corresponding "Before" values (e.g., 6 to 2, 8 to 3).- **Consistency**: The value "7" remains unchanged in both conditions.- **Minimal Change**: The pair 9 to 8 indicates the smallest reduction.This data could be representative of various scenarios such as a before-and-after experiment or a survey measuring impacts in educational environments.

(D) Step-by-step procedure to obtain the variance for difference (Before-After) using Excel is given below: In Excel sheet, enter Data in one column. In Data, select Data Analysis and choose Descriptive statistics. In Input Variable Range, select Data. Select Summary Statistics. Click Labels. Click Ok. Output obtained using the Excel is given below: From the output, the value of S2D is 8.(E) Step-by-step procedure to obtain the variance for Before and After using Excel is given below: In Excel sheet, enter Before and After in one column. In Data, select Data Analysis and choose Descriptive statistics. In Input Variable Range, select Before and After. Select Summary Statistics. Click Labels. Click Ok. Output obtained using the Excel is given below: From the output, the variance for before is 2.786 and the variance for after is 6.214. The value of S2 for the sampling distribution of Mean differences is 1.125, which is obtained below: S2=S12n1+S22n2=2.7868+6.2148=1.125 (F) From the output in Part (D), the value of the Standard error is 1.