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.
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.
Expert Solution
Step 1: Provide given information

Sample size n=972

Number of successes x=577

Confidence level 99%

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