Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 27 students, she finds 3 who eat cauliflower. Obtain and interpret a 90% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method. E Click the icon to view Agresti and Coull's method. Construct and interpret the 90% confidence interval. Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) O Agresti and Coull's method for constructing confidence intervals O A. There is a 90% chance that the proportion of students who eat cauliflower on Jane's campus is between and O B. The proportion of students who eat cauliflower on Jane's campus To deal with issues such as the distribution of p not following a normal distribution, A. Agresti and B. Coull proposed a modified approach to constructing confidence intervals for a proportion. A (1 - a) • 100% confidence interval for p is given by the between and 90% of the time. OC. One is 90% confident that the proportion of students who eat cauliflower on Jane's campus is between and O D. There is a 90% chance that the proportion of students who eat cauliflower in Jane's sample is between x+2 bounds shown below, where p= and x is the number successes inn trials. and. P(1-p) Lower bound: p-z,. n+4 p(1-P) Upper bound: p +z,. n+4
Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 27 students, she finds 3 who eat cauliflower. Obtain and interpret a 90% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method. E Click the icon to view Agresti and Coull's method. Construct and interpret the 90% confidence interval. Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) O Agresti and Coull's method for constructing confidence intervals O A. There is a 90% chance that the proportion of students who eat cauliflower on Jane's campus is between and O B. The proportion of students who eat cauliflower on Jane's campus To deal with issues such as the distribution of p not following a normal distribution, A. Agresti and B. Coull proposed a modified approach to constructing confidence intervals for a proportion. A (1 - a) • 100% confidence interval for p is given by the between and 90% of the time. OC. One is 90% confident that the proportion of students who eat cauliflower on Jane's campus is between and O D. There is a 90% chance that the proportion of students who eat cauliflower in Jane's sample is between x+2 bounds shown below, where p= and x is the number successes inn trials. and. P(1-p) Lower bound: p-z,. n+4 p(1-P) Upper bound: p +z,. n+4
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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![### Estimating the Proportion of Students Who Eat Cauliflower
**Scenario:**
Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 27 students, she finds 3 who eat cauliflower. She needs to obtain and interpret a 90% confidence interval for the proportion of students who eat cauliflower on her campus using Agresti and Coull’s method.
**Instructions:**
Construct and interpret the 90% confidence interval. Select the correct choice below and fill in the answer boxes within your choice. Remember to round to three decimal places as needed.
**Choices:**
A. There is a 90% chance that the proportion of students who eat cauliflower on Jane's campus is between [____] and [____].
B. The proportion of students who eat cauliflower on Jane's campus is between [____] and [____] 90% of the time.
C. One is 90% confident that the proportion of students who eat cauliflower on Jane's campus is between [____] and [____].
D. There is a 90% chance that the proportion of students who eat cauliflower in Jane's sample is between [____] and [____].
**Explanation of Agresti and Coull's Method:**
To deal with issues such as the distribution of \( \hat{p} \) not following a normal distribution, A. Agresti and B. Coull proposed a modified approach to constructing confidence intervals for a proportion. A \((1 - \alpha) \cdot 100\%\) confidence interval for \( p \) is given by the bounds shown below.
Where \( \tilde{p} = \frac{x + 2}{n + 4} \) and \( x \) is the number of successes in \( n \) trials.
- **Lower bound:**
\[
\tilde{p} - z_{\frac{\alpha}{2}} \sqrt{\frac{\tilde{p}(1 - \tilde{p})}{n + 4}}
\]
- **Upper bound:**
\[
\tilde{p} + z_{\frac{\alpha}{2}} \sqrt{\frac{\tilde{p}(1 - \tilde{p})}{n + 4}}
\]
**Graph/Diagram Description:**
On the right side, there is a window labeled "Agresti and Coull’s method](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4175707-d254-4126-a791-753312836f35%2Ff35a4cd6-91f8-441b-91c2-456db53f5b7e%2Foj6j3l_processed.png&w=3840&q=75)
Transcribed Image Text:### Estimating the Proportion of Students Who Eat Cauliflower
**Scenario:**
Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 27 students, she finds 3 who eat cauliflower. She needs to obtain and interpret a 90% confidence interval for the proportion of students who eat cauliflower on her campus using Agresti and Coull’s method.
**Instructions:**
Construct and interpret the 90% confidence interval. Select the correct choice below and fill in the answer boxes within your choice. Remember to round to three decimal places as needed.
**Choices:**
A. There is a 90% chance that the proportion of students who eat cauliflower on Jane's campus is between [____] and [____].
B. The proportion of students who eat cauliflower on Jane's campus is between [____] and [____] 90% of the time.
C. One is 90% confident that the proportion of students who eat cauliflower on Jane's campus is between [____] and [____].
D. There is a 90% chance that the proportion of students who eat cauliflower in Jane's sample is between [____] and [____].
**Explanation of Agresti and Coull's Method:**
To deal with issues such as the distribution of \( \hat{p} \) not following a normal distribution, A. Agresti and B. Coull proposed a modified approach to constructing confidence intervals for a proportion. A \((1 - \alpha) \cdot 100\%\) confidence interval for \( p \) is given by the bounds shown below.
Where \( \tilde{p} = \frac{x + 2}{n + 4} \) and \( x \) is the number of successes in \( n \) trials.
- **Lower bound:**
\[
\tilde{p} - z_{\frac{\alpha}{2}} \sqrt{\frac{\tilde{p}(1 - \tilde{p})}{n + 4}}
\]
- **Upper bound:**
\[
\tilde{p} + z_{\frac{\alpha}{2}} \sqrt{\frac{\tilde{p}(1 - \tilde{p})}{n + 4}}
\]
**Graph/Diagram Description:**
On the right side, there is a window labeled "Agresti and Coull’s method
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