MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Homework: Set - Prerequisite Week 6 **Question 2, IR.9.4** Check [here](#) for instructional material to complete this problem. --- #### Evaluate the following formula for: \[ p_1 - p_2 = 0 \] \[ \bar{p} = 0.164948, \quad \bar{q} = 1 - \bar{p} \] \[ x_1 = 79, \quad x_2 = 17 \] \[ n_1 = 295, \quad n_2 = 287 \] \[ \hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2} \] \[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_1} + \frac{\bar{p} \cdot \bar{q}}{n_2}}} \] \[ z = \boxed{\ \ \ \ \ \ \ \ \ \ \ } \quad \text{(Round to two decimal places as needed.)} \] --- **Explanation of the Formula:** 1. **\( \hat{p}_1 \) and \( \hat{p}_2 \)**: These are sample proportions calculated as: \[ \hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2} \] where \( x_1 \) and \( x_2 \) are the number of successes in each sample, and \( n_1 \) and \( n_2 \) are the sample sizes. 2. **\( \bar{p} \) and \( \bar{q} \)**: These are the pooled sample proportion and its complement. \[ \bar{q} = 1 - \bar{p} \] 3. **Z-Score Calculation**: \[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar
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Transcribed Image Text:### Homework: Set - Prerequisite Week 6 **Question 2, IR.9.4** Check [here](#) for instructional material to complete this problem. --- #### Evaluate the following formula for: \[ p_1 - p_2 = 0 \] \[ \bar{p} = 0.164948, \quad \bar{q} = 1 - \bar{p} \] \[ x_1 = 79, \quad x_2 = 17 \] \[ n_1 = 295, \quad n_2 = 287 \] \[ \hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2} \] \[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_1} + \frac{\bar{p} \cdot \bar{q}}{n_2}}} \] \[ z = \boxed{\ \ \ \ \ \ \ \ \ \ \ } \quad \text{(Round to two decimal places as needed.)} \] --- **Explanation of the Formula:** 1. **\( \hat{p}_1 \) and \( \hat{p}_2 \)**: These are sample proportions calculated as: \[ \hat{p}_1 = \frac{x_1}{n_1}, \quad \hat{p}_2 = \frac{x_2}{n_2} \] where \( x_1 \) and \( x_2 \) are the number of successes in each sample, and \( n_1 \) and \( n_2 \) are the sample sizes. 2. **\( \bar{p} \) and \( \bar{q} \)**: These are the pooled sample proportion and its complement. \[ \bar{q} = 1 - \bar{p} \] 3. **Z-Score Calculation**: \[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar
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