MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Estimating Sample Size for Population Proportion
To estimate a population proportion, you need to determine the appropriate sample size. Consider the following scenario:
**Scenario:**
- **Population Proportion (p):** Approximately 42%
- **Confidence Level:** 99%
- **Margin of Error:** 2.5%
**Question:**
How large of a sample size is required to ensure your estimate is within 2.5% of the true population proportion with 99% confidence?
**Hint:**
A linked video is provided to assist with this calculation.
**Input Field:**
You are prompted to input the calculated sample size (n) and submit your answer using the "Submit Question" button.
**Note:**
To calculate the sample size, you can use the formula for sample size estimation for proportions:
\[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \]
Where:
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( p \) is the estimated population proportion.
- \( E \) is the margin of error.
This exercise helps learners apply statistical concepts to real-world data analysis scenarios.](https://content.bartleby.com/qna-images/question/6aae277d-04e7-4ff7-b330-5dc8e3941ab0/0bd8a345-ff05-4bb7-936b-04fec92885cb/mb1nrx_processed.jpeg)
Transcribed Image Text:### Estimating Sample Size for Population Proportion
To estimate a population proportion, you need to determine the appropriate sample size. Consider the following scenario:
**Scenario:**
- **Population Proportion (p):** Approximately 42%
- **Confidence Level:** 99%
- **Margin of Error:** 2.5%
**Question:**
How large of a sample size is required to ensure your estimate is within 2.5% of the true population proportion with 99% confidence?
**Hint:**
A linked video is provided to assist with this calculation.
**Input Field:**
You are prompted to input the calculated sample size (n) and submit your answer using the "Submit Question" button.
**Note:**
To calculate the sample size, you can use the formula for sample size estimation for proportions:
\[ n = \left( \frac{Z^2 \times p \times (1-p)}{E^2} \right) \]
Where:
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( p \) is the estimated population proportion.
- \( E \) is the margin of error.
This exercise helps learners apply statistical concepts to real-world data analysis scenarios.
![Title: Determining Sample Size for Estimating a Population Mean
**Problem Statement:**
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately \( \sigma = 76.9 \). You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required?
**Interactive Element:**
- **Hint:**
- [Video] [](https://content.bartleby.com/qna-images/question/6aae277d-04e7-4ff7-b330-5dc8e3941ab0/0bd8a345-ff05-4bb7-936b-04fec92885cb/l45bj36_processed.jpeg)
Transcribed Image Text:Title: Determining Sample Size for Estimating a Population Mean
**Problem Statement:**
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately \( \sigma = 76.9 \). You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required?
**Interactive Element:**
- **Hint:**
- [Video] [
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