MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
### 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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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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