You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 28%. You would like to be 90% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required? Hint: Video [+] n =
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 28%. You would like to be 90% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required? Hint: Video [+] n =
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b2a9d04-6137-4cbe-9d79-c8370f802ff8%2F476ad02f-1f3f-45b0-950c-6cb6abdea0b0%2Fhtrvmiv_processed.jpeg&w=3840&q=75)
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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