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 2596 subjects randomly selected from an online group involved with ears. 963 surveys were returned. Construct a 95% confidence interval for the pro of returned surveys. Click the icon to view a table of z scores. 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.
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 2596 subjects randomly selected from an online group involved with ears. 963 surveys were returned. Construct a 95% confidence interval for the pro of returned surveys. Click the icon to view a table of z scores. 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
Related questions
Topic Video
Question
![**Confidence Interval Estimation for Population Proportion**
In the scenario provided, a study was conducted to examine cell phone use and brain hemispheric dominance. An Internet survey was sent to 2,596 randomly selected subjects from an online group involving ears. The number of surveys returned was 963. The task is to construct a 95% confidence interval for the proportion of returned surveys. Follow the steps below:
**(a) Find the Best Point Estimate of the Population Proportion \( p \).**
\[ \text{Point Estimate} = \frac{\text{Number of Returned Surveys}}{\text{Total Surveys Sent}} \]
- **Round to three decimal places as needed.**
**(b) Identify the Value of the Margin of Error \( E \).**
\[ E = z \times \sqrt{\frac{p(1-p)}{n}} \]
- **Round to three decimal places as needed.**
**(c) Construct the Confidence Interval.**
\[ \text{Confidence Interval: } p - E < p < p + E \]
- **Round to three decimal places as needed.**
**(d) Write a Statement that Correctly Interprets the Confidence Interval.**
Select the correct answer:
A. One has 95% confidence that the sample proportion is equal to the population proportion.
B. 95% of sample proportions will fall between the lower bound and the upper bound.
C. 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.
D. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
---
Click the icon to view a table of z scores for reference.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1111c530-3f2d-4037-a397-b2f78b1d84ff%2F81e63bc1-9213-45b1-aa83-c526fece701e%2Fl31eirh_processed.png&w=3840&q=75)
Transcribed Image Text:**Confidence Interval Estimation for Population Proportion**
In the scenario provided, a study was conducted to examine cell phone use and brain hemispheric dominance. An Internet survey was sent to 2,596 randomly selected subjects from an online group involving ears. The number of surveys returned was 963. The task is to construct a 95% confidence interval for the proportion of returned surveys. Follow the steps below:
**(a) Find the Best Point Estimate of the Population Proportion \( p \).**
\[ \text{Point Estimate} = \frac{\text{Number of Returned Surveys}}{\text{Total Surveys Sent}} \]
- **Round to three decimal places as needed.**
**(b) Identify the Value of the Margin of Error \( E \).**
\[ E = z \times \sqrt{\frac{p(1-p)}{n}} \]
- **Round to three decimal places as needed.**
**(c) Construct the Confidence Interval.**
\[ \text{Confidence Interval: } p - E < p < p + E \]
- **Round to three decimal places as needed.**
**(d) Write a Statement that Correctly Interprets the Confidence Interval.**
Select the correct answer:
A. One has 95% confidence that the sample proportion is equal to the population proportion.
B. 95% of sample proportions will fall between the lower bound and the upper bound.
C. 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.
D. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
---
Click the icon to view a table of z scores for reference.
![**Finding the Critical Value for a 97% Confidence Level**
To determine the critical value \( z_{\alpha/2} \) corresponding to a confidence level of 97%, follow these steps:
1. **Determine the Confidence Level**: The confidence level is given as 97%.
2. **Calculate \( \alpha \)**:
\[
\alpha = 1 - \text{Confidence Level} = 1 - 0.97 = 0.03
\]
3. **Find \( \alpha/2 \)**:
\[
\alpha/2 = 0.03 / 2 = 0.015
\]
4. **Locate the \( z \)-score**: To find \( z_{\alpha/2} \), use a standard normal distribution table or calculator to find the z-score that corresponds to the cumulative probability of \( 1 - 0.015 = 0.985 \).
5. **Round the Value**: Ensure that the critical value \( z_{\alpha/2} \) is rounded to two decimal places as needed.
By following these calculations, you can find the critical value \( z_{\alpha/2} \) which is required for constructing a 97% confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1111c530-3f2d-4037-a397-b2f78b1d84ff%2F81e63bc1-9213-45b1-aa83-c526fece701e%2F1m7n0qj_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Critical Value for a 97% Confidence Level**
To determine the critical value \( z_{\alpha/2} \) corresponding to a confidence level of 97%, follow these steps:
1. **Determine the Confidence Level**: The confidence level is given as 97%.
2. **Calculate \( \alpha \)**:
\[
\alpha = 1 - \text{Confidence Level} = 1 - 0.97 = 0.03
\]
3. **Find \( \alpha/2 \)**:
\[
\alpha/2 = 0.03 / 2 = 0.015
\]
4. **Locate the \( z \)-score**: To find \( z_{\alpha/2} \), use a standard normal distribution table or calculator to find the z-score that corresponds to the cumulative probability of \( 1 - 0.015 = 0.985 \).
5. **Round the Value**: Ensure that the critical value \( z_{\alpha/2} \) is rounded to two decimal places as needed.
By following these calculations, you can find the critical value \( z_{\alpha/2} \) which is required for constructing a 97% confidence interval.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
