Construct a confidence interval for p,-p2 at the given level of confidence. X1 = 358, n1 = 503, x2 = 413, n2 = 562, 95% 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 = 358, n1 = 503, x2 = 413, n2 = 562, 95% 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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![**Constructing a Confidence Interval for Population Proportions**
In this exercise, you will construct a confidence interval for the difference between two population proportions (\(p_1 - p_2\)) at a specified level of confidence.
**Given:**
- \(x_1 = 358\) (Number of successes in sample 1)
- \(n_1 = 503\) (Size of sample 1)
- \(x_2 = 413\) (Number of successes in sample 2)
- \(n_2 = 562\) (Size of sample 2)
- Level of Confidence: 95%
**Objective:**
Determine the range in which the difference between the two population proportions (\(p_1 - p_2\)) lies, with 95% confidence.
**Instructions:**
1. Calculate the sample proportions for both groups:
\[
\hat{p}_1 = \frac{x_1}{n_1}
\]
\[
\hat{p}_2 = \frac{x_2}{n_2}
\]
2. Use these sample proportions to construct the confidence interval for \(p_1 - p_2\).
3. The researchers are ___% confident that the difference in proportions is between ___ and ___. (Provide responses in ascending order and round to three decimal places as needed.)
This task will help you understand how to analyze sample data to make inferences about population parameters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc22cf0a8-395c-49f5-90ff-793ddbeecc12%2F59e13ab4-393a-48c3-b33d-eb029e2b7e43%2Fgwxzl25_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Constructing a Confidence Interval for Population Proportions**
In this exercise, you will construct a confidence interval for the difference between two population proportions (\(p_1 - p_2\)) at a specified level of confidence.
**Given:**
- \(x_1 = 358\) (Number of successes in sample 1)
- \(n_1 = 503\) (Size of sample 1)
- \(x_2 = 413\) (Number of successes in sample 2)
- \(n_2 = 562\) (Size of sample 2)
- Level of Confidence: 95%
**Objective:**
Determine the range in which the difference between the two population proportions (\(p_1 - p_2\)) lies, with 95% confidence.
**Instructions:**
1. Calculate the sample proportions for both groups:
\[
\hat{p}_1 = \frac{x_1}{n_1}
\]
\[
\hat{p}_2 = \frac{x_2}{n_2}
\]
2. Use these sample proportions to construct the confidence interval for \(p_1 - p_2\).
3. The researchers are ___% confident that the difference in proportions is between ___ and ___. (Provide responses in ascending order and round to three decimal places as needed.)
This task will help you understand how to analyze sample data to make inferences about population parameters.
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