A confidence interval for a population proportion p has been given. What was the sample proportion and what is the margin of error? 0.74 < p < 0.8
A confidence interval for a population proportion p has been given. What was the sample proportion and what is the margin of error? 0.74 < p < 0.8
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![**Understanding Confidence Intervals for Population Proportions**
A confidence interval for a population proportion \( p \) has been given. To determine crucial statistical measures, we ask: what was the sample proportion, and what is the margin of error?
**Given Confidence Interval:**
\[ 0.74 < p < 0.8 \]
**Questions:**
- What is the sample proportion (\(\hat{p}\))?
- What is the margin of error?
Use the provided space to input your calculations:
1. **Sample Proportion (\(\hat{p}\)):**
\(\hat{p} =\) [Input Box]
2. **Margin of Error:**
Margin of error = [Input Box]
**Calculating Sample Proportion:**
The sample proportion (\(\hat{p}\)) is the midpoint of the given confidence interval:
\[
\hat{p} = \frac{0.74 + 0.8}{2}
\]
**Calculating Margin of Error:**
The margin of error is half the width of the confidence interval:
\[
\text{Margin of error} = \frac{0.8 - 0.74}{2}
\]
By solving these equations, you will gain insights into the reliability and precision of your data estimates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab42d873-9f18-4f4e-9eaf-77750f86fa7d%2F87f6423a-1c65-4968-97a7-7f6d61432c9a%2Fg9ljpta_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Confidence Intervals for Population Proportions**
A confidence interval for a population proportion \( p \) has been given. To determine crucial statistical measures, we ask: what was the sample proportion, and what is the margin of error?
**Given Confidence Interval:**
\[ 0.74 < p < 0.8 \]
**Questions:**
- What is the sample proportion (\(\hat{p}\))?
- What is the margin of error?
Use the provided space to input your calculations:
1. **Sample Proportion (\(\hat{p}\)):**
\(\hat{p} =\) [Input Box]
2. **Margin of Error:**
Margin of error = [Input Box]
**Calculating Sample Proportion:**
The sample proportion (\(\hat{p}\)) is the midpoint of the given confidence interval:
\[
\hat{p} = \frac{0.74 + 0.8}{2}
\]
**Calculating Margin of Error:**
The margin of error is half the width of the confidence interval:
\[
\text{Margin of error} = \frac{0.8 - 0.74}{2}
\]
By solving these equations, you will gain insights into the reliability and precision of your data estimates.
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