### Confidence Interval Calculation for Poll Data**Scenario:**A research institute conducted a poll asking respondents if they felt vulnerable to identity theft. In this poll, with a sample size of $ n = 933 $, there were $ x = 562 $ respondents who said "yes." The analysis uses a 99% confidence level.#### Part (a): Compute the sample proportion $ \hat{p} $The sample proportion $ \hat{p} $ is given by:\[ \hat{p} = \frac{x}{n} = \frac{562}{933} \approx 0.602 \]_Rounded to three decimal places as needed._#### Part (b): Identify the value of the margin of error $ E $The margin of error $ E $ at a 99% confidence level can be calculated using the formula:\[ E = Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]For a 99% confidence level, $ Z_{\alpha/2} $ is typically 2.576. Given the sample proportion $ \hat{p} $ and sample size $ n $:\[ E \approx 0.041 \]_Rounded to three decimal places as needed._#### Part (c): Construct the confidence intervalThe confidence interval for the population proportion $ p $ can be calculated as:\[ \hat{p} - E < p < \hat{p} + E \]Substituting the values:\[ 0.602 - 0.041 < p < 0.602 + 0.041 \]\[ 0.561 < p < 0.644 \]_Rounded to three decimal places as needed._#### Part (d): Interpretation of the confidence intervalThe correct interpretation of this confidence interval is:- We are 99% confident that the true proportion of all respondents who feel vulnerable to identity theft is between 0.561 and 0.644.Feel free to use this structured data on your educational website to illustrate the process of calculating confidence intervals and interpreting statistical data obtained from polls.

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Description: ### Confidence Interval Calculation for Poll Data**Scenario:**A research institute conducted a poll asking respondents if they felt vulnerable to identity theft. In this poll, with a sample size of $ n = 933 $, there were $ x = 562 $ respondents

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Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 933 and x = 562 who said "yes." Use a 99% confidence level. E Click the icon to view a table of z scores. 0.602 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E = 0.041 (Round to three decimal places as needed.) c) Construct the confidence interval. 0.561

Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 933 and x = 562 who said "yes." Use a 99% confidence level. E Click the icon to view a table of z scores. 0.602 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E = 0.041 (Round to three decimal places as needed.) c) Construct the confidence interval. 0.561

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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