### Finding Confidence Intervals for Population Proportions**Instructions:**Use the sample data and confidence level given below to complete parts (a) through (d).**Scenario:**In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2,458 subjects randomly selected from an online group involved with ears. 962 surveys were returned. Construct a 95% confidence interval for the proportion of returned surveys.---#### Data Access:Click the icon to view a table of z-scores.---**Questions:****a) Find the best point estimate of the population proportion \( p \).**\[ \hat{p} = \frac{962}{2458} \approx 0.391 \]*(Round to three decimal places as needed.)*---**b) Identify the value of the margin of error \( E \).**\[ E = \square \]*(Round to three decimal places as needed.)*---**Additional details:**For part (a), the point estimate for the population proportion is calculated as the ratio of the number of returned surveys to the total number of surveys sent out.For part (b), the margin of error is typically calculated using the formula:\[ E = Z_{\frac{\alpha}{2}} \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]where:- \( Z_{\frac{\alpha}{2}} \) is the Z-score corresponding to the desired confidence level- \( \hat{p} \) is the sample proportion (0.391 in this case)- \( n \) is the sample size (2,458 in this case)One must refer to a z-score table for the critical value at the specified confidence level (for a 95% confidence interval, the critical value \( Z_{\frac{\alpha}{2}} \) is typically 1.96).Integrate these values to complete part (b).---**Practice:**Complete the calculations for part (b) using the given formula and the values provided in the prompt. This exercise will enhance your understanding of how to construct and interpret confidence intervals for population proportions.

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Use the sample data and confidence level given below to complete parts (a) through (d). In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2458 subjects randomly selected from an online group involved with ears. 962 surveys were returned. Construct a 95% confidence interval for the proportion of returned surveys.

Use the sample data and confidence level given below to complete parts (a) through (d). In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2458 subjects randomly selected from an online group involved with ears. 962 surveys were returned. Construct a 95% confidence interval for the proportion of returned surveys.

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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