A First Course in Probability (10th Edition)
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ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![### Estimating Sample Size for Population Proportion
To estimate a population proportion, it is essential to determine an appropriate sample size. Consider the following scenario for calculation purposes:
**Scenario:**
You want to obtain a sample to estimate a population proportion. Based on previous evidence, the population proportion is believed to be approximately 28%. You desire to be 90% confident that your estimate will be within 4.5% of the true population proportion. How large should your sample size be?
**Calculation:**
To perform this calculation, you can use the formula for sample size (n) in proportion estimation, which is:
\[ n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right) \]
Where:
- \( Z \): Z-score corresponding to your confidence level (for 90% confidence, \( Z \approx 1.645 \))
- \( p \): Estimated population proportion (0.28)
- \( E \): Margin of error or desired precision (0.045)
**Hint:** A detailed explanation can be found in the video provided [Video](https://content.bartleby.com/qna-images/question/8b2a9d04-6137-4cbe-9d79-c8370f802ff8/476ad02f-1f3f-45b0-950c-6cb6abdea0b0/htrvmiv_processed.jpeg)
Transcribed Image Text:### Estimating Sample Size for Population Proportion
To estimate a population proportion, it is essential to determine an appropriate sample size. Consider the following scenario for calculation purposes:
**Scenario:**
You want to obtain a sample to estimate a population proportion. Based on previous evidence, the population proportion is believed to be approximately 28%. You desire to be 90% confident that your estimate will be within 4.5% of the true population proportion. How large should your sample size be?
**Calculation:**
To perform this calculation, you can use the formula for sample size (n) in proportion estimation, which is:
\[ n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right) \]
Where:
- \( Z \): Z-score corresponding to your confidence level (for 90% confidence, \( Z \approx 1.645 \))
- \( p \): Estimated population proportion (0.28)
- \( E \): Margin of error or desired precision (0.045)
**Hint:** A detailed explanation can be found in the video provided [Video
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