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= 1039 and x= 511 who said "yes." Use a 95% confidence level. E Click the icon to view a table of z scores. .... a) Find the best point estimate of the population proportion p. 492 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E 030 (Round to three decimal places as needed.) c) Construct the confidence interval. 462
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= 1039 and x= 511 who said "yes." Use a 95% confidence level. E Click the icon to view a table of z scores. .... a) Find the best point estimate of the population proportion p. 492 (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E 030 (Round to three decimal places as needed.) c) Construct the confidence interval. 462
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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33
![**Using Sample Data and Confidence Level Analysis**
A research institute poll studied feelings of vulnerability to identity theft with the following data: sample size \( n = 1039 \), number of "yes" responses \( x = 511 \), and a confidence level of 95%.
**Tasks:**
a) **Determine the Best Point Estimate of the Population Proportion \( p \):**
- Calculation: \(\hat{p} = \frac{x}{n} = \frac{511}{1039} \approx 0.492\)
b) **Identify the Margin of Error \( E \):**
- Margin of Error: \( E = 0.030 \)
c) **Construct the Confidence Interval:**
- The 95% confidence interval for the population proportion \( p \) is \( 0.462 < p < 0.522 \).
d) **Interpret the Confidence Interval:**
- Correct Interpretation:
- A. One has 95% confidence that the interval from the lower bound to the upper bound actually contains the true value of the population proportion.
This solution includes a calculation of the point estimate, identification of the margin of error, construction of the confidence interval, and an interpretation to understand the meaning of these findings in statistical terms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Face2b3cd-4895-404b-9c09-22676e3afc9d%2F53599305-946a-4724-90fb-94704593e0be%2F9zdy2zw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Sample Data and Confidence Level Analysis**
A research institute poll studied feelings of vulnerability to identity theft with the following data: sample size \( n = 1039 \), number of "yes" responses \( x = 511 \), and a confidence level of 95%.
**Tasks:**
a) **Determine the Best Point Estimate of the Population Proportion \( p \):**
- Calculation: \(\hat{p} = \frac{x}{n} = \frac{511}{1039} \approx 0.492\)
b) **Identify the Margin of Error \( E \):**
- Margin of Error: \( E = 0.030 \)
c) **Construct the Confidence Interval:**
- The 95% confidence interval for the population proportion \( p \) is \( 0.462 < p < 0.522 \).
d) **Interpret the Confidence Interval:**
- Correct Interpretation:
- A. One has 95% confidence that the interval from the lower bound to the upper bound actually contains the true value of the population proportion.
This solution includes a calculation of the point estimate, identification of the margin of error, construction of the confidence interval, and an interpretation to understand the meaning of these findings in statistical terms.
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