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=972 and x = 577 who said "yes." Use a 99% confidence level. Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. 0.594 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. =0 (Round to three decimal places as needed.) E=
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=972 and x = 577 who said "yes." Use a 99% confidence level. Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. 0.594 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. =0 (Round to three decimal places as needed.) E=
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![### Statistical Analysis of Identity Theft Vulnerability
In a research institute poll, respondents were asked if they felt vulnerable to identity theft. The sample size was \( n = 972 \), with \( x = 577 \) individuals responding "yes." The analysis uses a 99% confidence level to determine the population proportion and margin of error.
#### Task Details:
1. **Best Point Estimate of Population Proportion (\( p \))**:
- The best point estimate for the population proportion \( p \) is calculated as follows:
\[
\hat{p} = \frac{x}{n} = \frac{577}{972} = 0.594
\]
- The estimate is rounded to three decimal places: **0.594**
2. **Margin of Error (\( E \))**:
- The margin of error formula accounts for the z-score corresponding to the chosen confidence level (99% in this case). However, the value is not provided in the document and requires further calculation using the formula:
\[
E = z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]
- Make sure to round \( E \) to three decimal places as needed.
For detailed calculations, a table of z scores should be referenced. This information is crucial for researchers and statisticians to accurately gauge public sentiment and the reliability of the poll results regarding identity theft vulnerability.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3b13e72-bc39-40fa-b794-559d1be8a70e%2F869ec78a-a859-44e1-8781-1f0520dd32f6%2Fbrx2spk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis of Identity Theft Vulnerability
In a research institute poll, respondents were asked if they felt vulnerable to identity theft. The sample size was \( n = 972 \), with \( x = 577 \) individuals responding "yes." The analysis uses a 99% confidence level to determine the population proportion and margin of error.
#### Task Details:
1. **Best Point Estimate of Population Proportion (\( p \))**:
- The best point estimate for the population proportion \( p \) is calculated as follows:
\[
\hat{p} = \frac{x}{n} = \frac{577}{972} = 0.594
\]
- The estimate is rounded to three decimal places: **0.594**
2. **Margin of Error (\( E \))**:
- The margin of error formula accounts for the z-score corresponding to the chosen confidence level (99% in this case). However, the value is not provided in the document and requires further calculation using the formula:
\[
E = z \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]
- Make sure to round \( E \) to three decimal places as needed.
For detailed calculations, a table of z scores should be referenced. This information is crucial for researchers and statisticians to accurately gauge public sentiment and the reliability of the poll results regarding identity theft vulnerability.
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