Express the confidence interval 0.111
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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Question 2
![**Instruction:**
Express the confidence interval \(0.111 < p < 0.999\) in the form \(\hat{p} \pm E\).
**Solution:**
To express this confidence interval in the standard form \(\hat{p} \pm E\):
1. **Calculate the Point Estimate \(\hat{p}\):**
\[
\hat{p} = \frac{0.111 + 0.999}{2} = 0.555
\]
2. **Calculate the Margin of Error \(E\):**
\[
E = \frac{0.999 - 0.111}{2} = 0.444
\]
**Result:**
\[
\hat{p} \pm E = 0.555 \pm 0.444
\]
This expression represents the confidence interval centered at \(\hat{p} = 0.555\) with a margin of error \(E = 0.444\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc517a8-8d25-4dba-b5b9-bbe3039266d7%2F92a75136-0b89-4309-8597-83ab8f6aa88d%2F1o4rcvg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction:**
Express the confidence interval \(0.111 < p < 0.999\) in the form \(\hat{p} \pm E\).
**Solution:**
To express this confidence interval in the standard form \(\hat{p} \pm E\):
1. **Calculate the Point Estimate \(\hat{p}\):**
\[
\hat{p} = \frac{0.111 + 0.999}{2} = 0.555
\]
2. **Calculate the Margin of Error \(E\):**
\[
E = \frac{0.999 - 0.111}{2} = 0.444
\]
**Result:**
\[
\hat{p} \pm E = 0.555 \pm 0.444
\]
This expression represents the confidence interval centered at \(\hat{p} = 0.555\) with a margin of error \(E = 0.444\).
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