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
Related questions
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman