Pair 1 2 3 4 5 6 7 8 9 mean SD Alcoholic 40.1 38.5 36.9 41.4 40.6 42.3 37.2 38.6 38.5 39.344 1.860 Control 41.3 40.2 37.4 46.1 43.9 41.9 39.9 40.4 38.6 41.078 2.650 Difference -1.2 -1.7 -0.5 -4.7 -3.3 0.4 -2.7 -1.8 -0.1 In an investigation of possible brain damage due to alcoholism, an X-ray procedure known as a computerized tomography (CT) scan was used to measure brain densities in 9 chronic alcoholics. For each alcoholic, a nonalcoholic control was selected who matched the alcoholic on age, sex, education, and other factors. The brain density measurements on the alcoholics and the matched controls are reported in the accompanying table. A). Assuming the data are normally distributed, please use the appropriate t-test to determine whether the mean brain density is different across alcoholic or nonalcoholic people. Use a = 0.05. Clearly state the null and alternative hypothesis, then calculate the t-test and P-value, and show your hypothesis decision and conclusion. B). If the data are not normally distributed, please use the Wilcoxon Signed Rank Test to determine whether the mean brain density is different across alcoholic or nonalcoholic people. Use a = 0.05. Clearly state the null and alternative hypothesis, then calculate the Wilcoxon signed-rank test value and P-value, and show your hypothesis decision and conclusion. -1.733 1.629
Pair 1 2 3 4 5 6 7 8 9 mean SD Alcoholic 40.1 38.5 36.9 41.4 40.6 42.3 37.2 38.6 38.5 39.344 1.860 Control 41.3 40.2 37.4 46.1 43.9 41.9 39.9 40.4 38.6 41.078 2.650 Difference -1.2 -1.7 -0.5 -4.7 -3.3 0.4 -2.7 -1.8 -0.1 In an investigation of possible brain damage due to alcoholism, an X-ray procedure known as a computerized tomography (CT) scan was used to measure brain densities in 9 chronic alcoholics. For each alcoholic, a nonalcoholic control was selected who matched the alcoholic on age, sex, education, and other factors. The brain density measurements on the alcoholics and the matched controls are reported in the accompanying table. A). Assuming the data are normally distributed, please use the appropriate t-test to determine whether the mean brain density is different across alcoholic or nonalcoholic people. Use a = 0.05. Clearly state the null and alternative hypothesis, then calculate the t-test and P-value, and show your hypothesis decision and conclusion. B). If the data are not normally distributed, please use the Wilcoxon Signed Rank Test to determine whether the mean brain density is different across alcoholic or nonalcoholic people. Use a = 0.05. Clearly state the null and alternative hypothesis, then calculate the Wilcoxon signed-rank test value and P-value, and show your hypothesis decision and conclusion. -1.733 1.629
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Title: Investigation of Brain Density Differences Due to Alcoholism Using CT Scans**
**Overview:**
In an investigation of possible brain damage due to alcoholism, a computerized tomography (CT) scan was used to measure brain densities in 9 chronic alcoholics. For each alcoholic, a nonalcoholic control was selected who matched the alcoholic on age, sex, education, and other factors. The brain density measurements for the alcoholics and the matched controls are reported in the accompanying table below:
| Pair | Alcoholic | Control | Difference |
|------|-----------|---------|------------|
| 1 | 40.1 | 41.3 | -1.2 |
| 2 | 38.5 | 40.2 | -1.7 |
| 3 | 36.9 | 37.4 | -0.5 |
| 4 | 41.4 | 46.1 | -4.7 |
| 5 | 40.6 | 43.9 | -3.3 |
| 6 | 42.8 | 41.9 | 0.4 |
| 7 | 37.2 | 39.9 | -2.7 |
| 8 | 38.6 | 40.4 | -1.8 |
| 9 | 38.5 | 38.6 | -0.1 |
| | | Mean | SD |
|------|-----------|---------|------------|
| Mean | | 41.078 | 1.629 |
| SD | | 2.650 | 1.629 |
### Tasks:
**A) Hypothesis Testing with Normally Distributed Data:**
- **Objective:** Determine whether the mean brain density differs between alcoholic and nonalcoholic people.
- **Procedure:** Use the appropriate t-test.
- **Significance Level (α):** 0.05
- **Steps:**
1. **State the Null Hypothesis (H₀):** The mean brain density of alcoholics is equal to that of nonalcoholics.
2. **State the Alternative Hypothesis (H₁):** The mean brain density of alcohol
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