Express the confidence interval 0.555 < p<0.777 in the form ptE. ptE=
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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![**Transcription of Educational Content:**
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**Express the Confidence Interval in the Form \(\hat{p} \pm E\):**
The task is to express the given confidence interval \(0.555 < p < 0.777\) in the form \(\hat{p} \pm E\).
\[ \hat{p} \pm E = \boxed{\ \ \ } \pm \boxed{\ \ \ } \]
---
**Explanation:**
This section is focused on converting a given confidence interval into a standard expression involving the point estimate \(\hat{p}\) and the margin of error \(E\).
1. **Calculate \(\hat{p}\):** It is the midpoint of the confidence interval. Calculate it using the formula:
\[
\hat{p} = \frac{\text{Lower bound} + \text{Upper bound}}{2} = \frac{0.555 + 0.777}{2}
\]
2. **Calculate \(E\):** It is half the width of the confidence interval. Calculate it using the formula:
\[
E = \frac{\text{Upper bound} - \text{Lower bound}}{2} = \frac{0.777 - 0.555}{2}
\]
This will provide the values to fill in the provided expression for \(\hat{p} \pm E\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F626680b8-87a8-442c-b0ab-f04aa1b187bb%2F0391dbff-c63d-40d2-bbbf-eff1ede80d11%2Fxw0rmfh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription of Educational Content:**
---
**Express the Confidence Interval in the Form \(\hat{p} \pm E\):**
The task is to express the given confidence interval \(0.555 < p < 0.777\) in the form \(\hat{p} \pm E\).
\[ \hat{p} \pm E = \boxed{\ \ \ } \pm \boxed{\ \ \ } \]
---
**Explanation:**
This section is focused on converting a given confidence interval into a standard expression involving the point estimate \(\hat{p}\) and the margin of error \(E\).
1. **Calculate \(\hat{p}\):** It is the midpoint of the confidence interval. Calculate it using the formula:
\[
\hat{p} = \frac{\text{Lower bound} + \text{Upper bound}}{2} = \frac{0.555 + 0.777}{2}
\]
2. **Calculate \(E\):** It is half the width of the confidence interval. Calculate it using the formula:
\[
E = \frac{\text{Upper bound} - \text{Lower bound}}{2} = \frac{0.777 - 0.555}{2}
\]
This will provide the values to fill in the provided expression for \(\hat{p} \pm E\).
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