b. a 95% confidence interval on the estimate of 75% and interpretation. Proportion (p) =0.75 Confidence level 95%
b. a 95% confidence interval on the estimate of 75% and interpretation. Proportion (p) =0.75 Confidence level 95%
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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Use answers to Q3b to determine a
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![**Constructing a 95% Confidence Interval for a Proportion Estimate and Its Interpretation**
To determine a 95% confidence interval for the population proportion:
- **Proportion (\(\hat{p}\))**: 0.75
- **Confidence level**: 95%
- **Margin of error**: 0.03
- **Sample size (\(n\))**: 850
**Steps to Construct a 95% Confidence Interval:**
We aim to calculate the 95% confidence interval regarding the population proportion. The confidence interval estimation is given by:
\[
CI = \hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]
**Calculation:**
\[
CI = 0.75 \pm (1.96) \sqrt{\frac{0.75(1-0.75)}{850}}
\]
\[
= 0.75 \pm 0.0291
\]
\[
= (0.7209, 0.7791)
\]
The confidence interval ranges from 0.7209 to 0.7791. This means we are 95% confident that the true population proportion lies within this interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f26ed86-dcd4-440f-94e9-1bdcbc6c4942%2Fd9f876d1-5f43-42b6-92fc-e624c996781c%2F3ep3u5e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Constructing a 95% Confidence Interval for a Proportion Estimate and Its Interpretation**
To determine a 95% confidence interval for the population proportion:
- **Proportion (\(\hat{p}\))**: 0.75
- **Confidence level**: 95%
- **Margin of error**: 0.03
- **Sample size (\(n\))**: 850
**Steps to Construct a 95% Confidence Interval:**
We aim to calculate the 95% confidence interval regarding the population proportion. The confidence interval estimation is given by:
\[
CI = \hat{p} \pm z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}
\]
**Calculation:**
\[
CI = 0.75 \pm (1.96) \sqrt{\frac{0.75(1-0.75)}{850}}
\]
\[
= 0.75 \pm 0.0291
\]
\[
= (0.7209, 0.7791)
\]
The confidence interval ranges from 0.7209 to 0.7791. This means we are 95% confident that the true population proportion lies within this interval.
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