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 = 995 and x = 532 who said "yes." Use a 99% confidence level. Click the icon to view a table of z scores. C a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E= (Round to three decimal places as needed.) c) Construct the confidence interval.
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 = 995 and x = 532 who said "yes." Use a 99% confidence level. Click the icon to view a table of z scores. C a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.) b) Identify the value of the margin of error E. E= (Round to three decimal places as needed.) c) Construct the confidence interval.
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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Question
![**Using Sample Data and Confidence Levels to Estimate Population Parameters**
**Context:**
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, \( n = 995 \) and \( x = 532 \) who said "yes." Use a 99% confidence level.
[Click the icon to view a table of z scores.]
---
**Instructions and Calculations:**
**a) Find the best point estimate of the population proportion \( p \).**
\[
\text{(Round to three decimal places as needed)}
\]
[Input box]
**b) Identify the value of the margin of error \( E \).**
\[
E =
\]
\[
\text{(Round to three decimal places as needed)}
\]
[Input box]
**c) Construct the confidence interval.**
\[
< p <
\]
\[
\text{(Round to three decimal places as needed)}
\]
[Left input box] - [Right input box]
**d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.**
- A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
- B. 99% of sample proportions will fall between the lower bound and the upper bound.
- C. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
- D. One has 99% confidence that the sample proportion is equal to the population proportion.
[Option A is selected]
---
**Explanation of Concepts in the Example:**
- **Point Estimate:** This is the best single estimate of the population proportion, calculated as \( \hat{p} = \frac{x}{n} \).
- **Margin of Error (E):** This value determines the range around the point estimate in which the true population proportion is likely to lie.
- **Confidence Interval:** This interval (between lower and upper bounds) provides a range of values which, with a certain level of confidence (in this case, 99%), contains the true population proportion.
- **Interpretation of Confidence Interval:** Understanding what the confidence interval means helps in making informed conclusions about the population based on sample data.
Use this process to estimate population parameters](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa19999fe-5ff0-4da5-8e70-0a6e9b11cafb%2F9bf67777-5b86-4f8a-a7be-2d934b64d13b%2F06bkt1_processed.png&w=3840&q=75)
Transcribed Image Text:**Using Sample Data and Confidence Levels to Estimate Population Parameters**
**Context:**
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, \( n = 995 \) and \( x = 532 \) who said "yes." Use a 99% confidence level.
[Click the icon to view a table of z scores.]
---
**Instructions and Calculations:**
**a) Find the best point estimate of the population proportion \( p \).**
\[
\text{(Round to three decimal places as needed)}
\]
[Input box]
**b) Identify the value of the margin of error \( E \).**
\[
E =
\]
\[
\text{(Round to three decimal places as needed)}
\]
[Input box]
**c) Construct the confidence interval.**
\[
< p <
\]
\[
\text{(Round to three decimal places as needed)}
\]
[Left input box] - [Right input box]
**d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.**
- A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
- B. 99% of sample proportions will fall between the lower bound and the upper bound.
- C. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
- D. One has 99% confidence that the sample proportion is equal to the population proportion.
[Option A is selected]
---
**Explanation of Concepts in the Example:**
- **Point Estimate:** This is the best single estimate of the population proportion, calculated as \( \hat{p} = \frac{x}{n} \).
- **Margin of Error (E):** This value determines the range around the point estimate in which the true population proportion is likely to lie.
- **Confidence Interval:** This interval (between lower and upper bounds) provides a range of values which, with a certain level of confidence (in this case, 99%), contains the true population proportion.
- **Interpretation of Confidence Interval:** Understanding what the confidence interval means helps in making informed conclusions about the population based on sample data.
Use this process to estimate population parameters
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