Use the sample data and confidence level given below to complete parts (a) through (d). In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2652 subjects randomly selected from an online group involved with ears. 905 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys. Click the icon to view a table of z scores. (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. 0
Use the sample data and confidence level given below to complete parts (a) through (d). In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2652 subjects randomly selected from an online group involved with ears. 905 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys. Click the icon to view a table of z scores. (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. 0
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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![**Using a Study to Construct a 99% Confidence Interval for Proportion of Returned Surveys**
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2652 subjects randomly selected from an online group involved with ears. 905 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys.
**a) Find the sample proportion.**
\[ \hat{p} = \frac{905}{2652} \]
\[ \hat{p} \approx 0.341 \]
(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.**
\[ \hat{p} - E < p < \hat{p} + E \]
(Round to three decimal places as needed.)
**d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.**
- A. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
- B. 99% of sample proportions will fall between the lower bound and the upper bound.
- C. One has 99% confidence that the sample proportion is equal to the population proportion.
- D. 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.
**The correct answer is:**
- **D. 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.**
Note: The question involves calculating the sample proportion, margin of error, constructing the confidence interval, and interpreting it. It refers to using a table of z-scores to find the critical value for a 99% confidence level, which is a standard procedure in constructing confidence intervals for proportions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc18b90ea-cb53-41e6-9532-f9af83d8e951%2Fa01f667e-26d5-49a3-a76f-d50a5edd85d2%2Fesw3iw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using a Study to Construct a 99% Confidence Interval for Proportion of Returned Surveys**
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2652 subjects randomly selected from an online group involved with ears. 905 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys.
**a) Find the sample proportion.**
\[ \hat{p} = \frac{905}{2652} \]
\[ \hat{p} \approx 0.341 \]
(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.**
\[ \hat{p} - E < p < \hat{p} + E \]
(Round to three decimal places as needed.)
**d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.**
- A. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
- B. 99% of sample proportions will fall between the lower bound and the upper bound.
- C. One has 99% confidence that the sample proportion is equal to the population proportion.
- D. 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.
**The correct answer is:**
- **D. 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.**
Note: The question involves calculating the sample proportion, margin of error, constructing the confidence interval, and interpreting it. It refers to using a table of z-scores to find the critical value for a 99% confidence level, which is a standard procedure in constructing confidence intervals for proportions.
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