### Confidence Interval Calculation for Proportion Differences#### Given Data:Two samples are taken with the following numbers of successes and sample sizes:- \( x_1 = 36 \)- \( x_2 = 23 \)- \( n_1 = 59 \)- \( n_2 = 53 \)#### Objective:Find a 96% confidence interval for the difference in proportions \( p_1 - p_2 \). Round the answers to the nearest thousandth.#### Instructions:- Calculate the sample proportions: \( \hat{p}_1 \) and \( \hat{p}_2 \).- Use the formula for the confidence interval of the difference between two proportions. #### Formula:\[\text{Confidence Interval} = (\hat{p}_1 - \hat{p}_2) \pm Z \sqrt{\left(\frac{\hat{p}_1(1 - \hat{p}_1)}{n_1}\right) + \left(\frac{\hat{p}_2(1 - \hat{p}_2)}{n_2}\right)}\]Where:- \( \hat{p}_1 = \frac{x_1}{n_1} \)- \( \hat{p}_2 = \frac{x_2}{n_2} \)- \( Z \) is the Z-value corresponding to the desired confidence level (for 96%, Z ≈ 2.05).#### Steps:1. Calculate \( \hat{p}_1 \) and \( \hat{p}_2 \): \[ \hat{p}_1 = \frac{36}{59}, \quad \hat{p}_2 = \frac{23}{53} \]2. Find the standard error (SE) for the difference in proportions: \[ SE = \sqrt{\left(\frac{\hat{p}_1(1 - \hat{p}_1)}{59}\right) + \left(\frac{\hat{p}_2(1 - \hat{p}_2)}{53}\right)} \]3. Multiply the SE by the Z-value for 96% confidence and apply to the difference in sample proportions to find the confidence interval: \[ \text{Confidence Interval} = (\hat{p}_1 - \hat{p}_2) \pm

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Description: ### Confidence Interval Calculation for Proportion Differences#### Given Data:Two samples are taken with the following numbers of successes and sample sizes:- \( x_1 = 36 \)- \( x_2 = 23 \)- \( n_1 = 59 \)- \( n_2 = 53 \)#### Objective:Find a 96% co

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Answered: Two samples are taken with the…

Math

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Two samples are taken with the following numbers of successes and sample sizes x1 = 36 x2 = 23 n1 = 59 n2 = 53 Find a 96% confidence interval, round answers to the nearest thousandth. < pi – P2 <

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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