### Constructing a Confidence Interval for the Difference in Population ProportionsIn this lesson, we will learn how to construct a confidence interval for the difference between two population proportions, \( p_1 - p_2 \), using the given data and a specified confidence level. This is useful when you want to compare two groups and understand the range in which the true difference in their proportions lies with a certain level of confidence.#### Given Data:- \( x_1 = 387 \)- \( n_1 = 536 \)- \( x_2 = 415 \)- \( n_2 = 551 \)- Confidence level: 90%#### Step-by-Step Process:1. **Identify the given values**: - \( x_1 \) and \( n_1 \) are the sample successes and sample size for the first population. - \( x_2 \) and \( n_2 \) are the sample successes and sample size for the second population.2. **Calculate the sample proportions**: - Sample proportion for the first population: \( \hat{p}_1 = \frac{x_1}{n_1} \) - Sample proportion for the second population: \( \hat{p}_2 = \frac{x_2}{n_2} \)3. **Determine the difference between the sample proportions**: - Difference: \( \hat{p}_1 - \hat{p}_2 \)4. **Calculate the standard error of the difference between the two proportions**: - Standard Error (SE): \( \sqrt{\frac{\hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{\hat{p}_2 (1 - \hat{p}_2)}{n_2}} \)5. **Find the Z-score corresponding to the 90% confidence level**: - Z-score for 90% confidence is typically 1.645 (this can be found from Z-tables or statistical tools)6. **Calculate the margin of error**: - Margin of Error (ME): \( Z \times SE \)7. **Construct the confidence interval**: - Lower bound: \( (\hat{p}_1 - \hat{p}_2) - ME \) - Upper bound: \( (\hat{p}_1 - \hat{p

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Description: ### Constructing a Confidence Interval for the Difference in Population ProportionsIn this lesson, we will learn how to construct a confidence interval for the difference between two population proportions, \( p_1 - p_2 \), using the given data and

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Construct a confidence interval for p, -P2 at the given level of confidence. X1 = 387, n, = 536, x2 = 415, n2 = 551, 90% confidence The researchers are % confident the difference between the two population proportions, p, -P2, is between and (Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)

Construct a confidence interval for p, -P2 at the given level of confidence. X1 = 387, n, = 536, x2 = 415, n2 = 551, 90% confidence The researchers are % confident the difference between the two population proportions, p, -P2, is between and (Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)

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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