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
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Author:Amos Gilat
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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.
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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