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=D (Round to three decimal places as needed.) c) Construct the confidence interval.
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=D (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
3
![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.
- Click the icon to view a table of z scores.
**a)** Find the best point estimate of the population proportion \( p \).
\[ \Box \]
(Round to three decimal places as needed.)
**b)** Identify the value of the margin of error \( E \).
\[ E = \Box \]
(Round to three decimal places as needed.)
**c)** Construct the confidence interval.
\[ \Box < p < \Box \]
(Round to three decimal places as needed.)
**d)** Write a statement that correctly interprets the confidence interval. Choose the correct answer below:
- \( \bigcirc \) A. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
- \( \bigcirc \) B. One has 95% confidence that the sample proportion is equal to the population proportion.
- \( \bigcirc \) C. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
- \( \bigcirc \) D. 95% of sample proportions will fall between the lower bound and the upper bound.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Face2b3cd-4895-404b-9c09-22676e3afc9d%2F335fdff5-f593-480e-b2ee-86a3d67f9f3a%2Fbed7s_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
- Click the icon to view a table of z scores.
**a)** Find the best point estimate of the population proportion \( p \).
\[ \Box \]
(Round to three decimal places as needed.)
**b)** Identify the value of the margin of error \( E \).
\[ E = \Box \]
(Round to three decimal places as needed.)
**c)** Construct the confidence interval.
\[ \Box < p < \Box \]
(Round to three decimal places as needed.)
**d)** Write a statement that correctly interprets the confidence interval. Choose the correct answer below:
- \( \bigcirc \) A. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
- \( \bigcirc \) B. One has 95% confidence that the sample proportion is equal to the population proportion.
- \( \bigcirc \) C. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
- \( \bigcirc \) D. 95% of sample proportions will fall between the lower bound and the upper bound.
Expert Solution
Step 1
Given that
Sample size n = 1039
Number of people who said yes, X = 511
The critical value of Z at 95% confidence level is 1.96
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