Express the confidence interval (13.8 %, 20 %) in the form of p + E.
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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![### Expressing Confidence Intervals
To express the confidence interval (13.8%, 20%) in the form of \( \hat{p} \pm E \), follow the steps below:
1. **Calculate \( \hat{p} \)**:
- \( \hat{p} \) is the midpoint of the confidence interval.
- Formula: \( \hat{p} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \)
- Calculation: \( \hat{p} = \frac{13.8\% + 20\%}{2} = 16.9\% \)
2. **Calculate \( E \)**:
- \( E \) is the margin of error.
- Formula: \( E = \text{Upper limit} - \hat{p} \) or \( E = \hat{p} - \text{Lower limit} \)
- Calculation: \( E = 20\% - 16.9\% = 3.1\% \)
3. **Express the interval in the form of \( \hat{p} \pm E \)**:
- Result: \( 16.9\% \pm 3.1\% \)
Below this explanation, there are two boxes to fill in the calculated values:
**Boxes Explanation:**
- The first box is for \( \hat{p} \), which should be filled with **16.9%**.
- The second box is for \( E \), which should be filled with **3.1%**.
### Visual Explanation
- **Input Boxes:**
- The left box: "16.9%"
- The right box: "3.1%"
This helps in visualizing and properly expressing confidence intervals in a precise mathematical format.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb954a688-5e54-4f96-9877-503883322f61%2Fb7311122-2ce8-46ff-963d-669b0fc209cf%2Fftf4w5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Expressing Confidence Intervals
To express the confidence interval (13.8%, 20%) in the form of \( \hat{p} \pm E \), follow the steps below:
1. **Calculate \( \hat{p} \)**:
- \( \hat{p} \) is the midpoint of the confidence interval.
- Formula: \( \hat{p} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \)
- Calculation: \( \hat{p} = \frac{13.8\% + 20\%}{2} = 16.9\% \)
2. **Calculate \( E \)**:
- \( E \) is the margin of error.
- Formula: \( E = \text{Upper limit} - \hat{p} \) or \( E = \hat{p} - \text{Lower limit} \)
- Calculation: \( E = 20\% - 16.9\% = 3.1\% \)
3. **Express the interval in the form of \( \hat{p} \pm E \)**:
- Result: \( 16.9\% \pm 3.1\% \)
Below this explanation, there are two boxes to fill in the calculated values:
**Boxes Explanation:**
- The first box is for \( \hat{p} \), which should be filled with **16.9%**.
- The second box is for \( E \), which should be filled with **3.1%**.
### Visual Explanation
- **Input Boxes:**
- The left box: "16.9%"
- The right box: "3.1%"
This helps in visualizing and properly expressing confidence intervals in a precise mathematical format.
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