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.

Answered: A researcher would like to evaluate the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 S²_D

E. Calculate S²for the sampling distribution of Mean differences

F. Calculate Standard error

### Data Comparison: Before and After

The 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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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