Use the sample data and confidence level given below to complete parts (a) through (d). K A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=929 and x = 582 who said "yes." Use a 95% confidence level. Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. * 0.626 (Round to three decimal places as needed.) b) Identify the value of the margin of error E E=Q (Round to three decimal places as needed.).
Use the sample data and confidence level given below to complete parts (a) through (d). K A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=929 and x = 582 who said "yes." Use a 95% confidence level. Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. * 0.626 (Round to three decimal places as needed.) b) Identify the value of the margin of error E E=Q (Round 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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![**Statistics Exercise: Estimating Population Proportion with Confidence Intervals**
In this exercise, we are analyzing data from a research institute poll regarding identity theft vulnerability. The poll includes responses from 929 individuals, with 582 indicating that they feel vulnerable to identity theft. We will use a 95% confidence level for our estimations.
### Instructions:
**a) Find the best point estimate of the population proportion \( p \):**
- The best point estimate of the population proportion \( p \) is calculated using the formula:
\[
\hat{p} = \frac{x}{n}
\]
where \( x = 582 \) (the number of respondents who said "yes") and \( n = 929 \) (the total number of respondents).
- **Point Estimate:**
\[
\hat{p} = \frac{582}{929} = 0.626
\]
*(Round to three decimal places as needed.)*
**b) Identify the value of the margin of error \( E \):**
- The margin of error \( E \) can be determined using the formula:
\[
E = Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]
where \( Z \) is the Z-score for the chosen confidence level (for 95%, \( Z \approx 1.96 \)).
- **Margin of Error Calculation:**
- First, calculate the standard error:
\[
SE = \sqrt{\frac{0.626 \times (1-0.626)}{929}}
\]
- Then multiply by the Z-score to find \( E \).
*(Round the margin of error to three decimal places as needed.)*
### Additional Resources:
- To find Z-scores for various confidence levels, you may refer to a table of Z-scores.
This exercise provides a practical application of calculating point estimates and confidence intervals, essential concepts in statistical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38d7ad60-cd84-472c-8996-4a82bb3a3198%2F7ee0cc9f-9909-41e7-8d1d-14b1450cb2bb%2F29an57i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Statistics Exercise: Estimating Population Proportion with Confidence Intervals**
In this exercise, we are analyzing data from a research institute poll regarding identity theft vulnerability. The poll includes responses from 929 individuals, with 582 indicating that they feel vulnerable to identity theft. We will use a 95% confidence level for our estimations.
### Instructions:
**a) Find the best point estimate of the population proportion \( p \):**
- The best point estimate of the population proportion \( p \) is calculated using the formula:
\[
\hat{p} = \frac{x}{n}
\]
where \( x = 582 \) (the number of respondents who said "yes") and \( n = 929 \) (the total number of respondents).
- **Point Estimate:**
\[
\hat{p} = \frac{582}{929} = 0.626
\]
*(Round to three decimal places as needed.)*
**b) Identify the value of the margin of error \( E \):**
- The margin of error \( E \) can be determined using the formula:
\[
E = Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]
where \( Z \) is the Z-score for the chosen confidence level (for 95%, \( Z \approx 1.96 \)).
- **Margin of Error Calculation:**
- First, calculate the standard error:
\[
SE = \sqrt{\frac{0.626 \times (1-0.626)}{929}}
\]
- Then multiply by the Z-score to find \( E \).
*(Round the margin of error to three decimal places as needed.)*
### Additional Resources:
- To find Z-scores for various confidence levels, you may refer to a table of Z-scores.
This exercise provides a practical application of calculating point estimates and confidence intervals, essential concepts in statistical analysis.
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