Express the confidence interval (0.042,0.136) 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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Question
![**MAT 135 Rattray**
**Homework: Chapter ... Question 4, 7.1.11**
**Task:**
Express the confidence interval (0.042, 0.136) in the form of \(\hat{p} - E < p < \hat{p} + E\).
**Input box:**
\(\_ < p < \_\) (Type integers or decimals.)
**Guidelines for solving this problem:**
1. **Identify the Confidence Interval:** The given interval is (0.042, 0.136).
2. **Calculate the Point Estimate (\(\hat{p}\)):**
- The point estimate is the midpoint of the interval, calculated as:
\[
\hat{p} = \frac{0.042 + 0.136}{2}
\]
3. **Determine the Margin of Error (E):**
- The margin of error is the distance from the point estimate to either endpoint of the interval, calculated as:
\[
E = \hat{p} - 0.042 \quad \text{or} \quad E = 0.136 - \hat{p}
\]
4. **Express the Interval:**
- Substitute the calculated values of \(\hat{p}\) and \(E\) into the inequality:
\[
\hat{p} - E < p < \hat{p} + E
\]
**Instructions:** Enter the appropriate values for the lower and upper bounds of \(p\) in the input boxes provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4311afe-187b-40d8-a31a-3b5ac958ea7b%2Fd8c513aa-67e1-45ef-9da3-9f4f4083ccdc%2Fwz4om6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**MAT 135 Rattray**
**Homework: Chapter ... Question 4, 7.1.11**
**Task:**
Express the confidence interval (0.042, 0.136) in the form of \(\hat{p} - E < p < \hat{p} + E\).
**Input box:**
\(\_ < p < \_\) (Type integers or decimals.)
**Guidelines for solving this problem:**
1. **Identify the Confidence Interval:** The given interval is (0.042, 0.136).
2. **Calculate the Point Estimate (\(\hat{p}\)):**
- The point estimate is the midpoint of the interval, calculated as:
\[
\hat{p} = \frac{0.042 + 0.136}{2}
\]
3. **Determine the Margin of Error (E):**
- The margin of error is the distance from the point estimate to either endpoint of the interval, calculated as:
\[
E = \hat{p} - 0.042 \quad \text{or} \quad E = 0.136 - \hat{p}
\]
4. **Express the Interval:**
- Substitute the calculated values of \(\hat{p}\) and \(E\) into the inequality:
\[
\hat{p} - E < p < \hat{p} + E
\]
**Instructions:** Enter the appropriate values for the lower and upper bounds of \(p\) in the input boxes provided.
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