You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 76.5. You would like to be 95% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Hint: Video [+] n =
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 76.5. You would like to be 95% confident that your estimate is within 1 of the true population mean. 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
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**Formula for Sample Size (n):**
\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]
- Z is the z-value corresponding to the desired confidence level (for 95%, Z = 1.96)
- σ is the population standard deviation
- E is the margin of error
**Calculation:**
\[ n = \left( \frac{1.96 \cdot 76.5}{1} \right)^2 \]
Here, you need to:
1. Multiply the Z value by the population standard deviation.
2. Divide the product by the margin of error.
3. Square the result to get the sample size.
After completing the calculation, fill in the sample size in the box below:
\[ n = \boxed{} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b2a9d04-6137-4cbe-9d79-c8370f802ff8%2Fdc3c1bb2-7d34-4d7e-911e-c55e5cb64332%2F7uaw6va_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining Sample Size for Estimating a Population Mean
You aim to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation (σ) is approximately 76.5. You would like to be 95% confident that your estimate is within 1 of the true population mean. How large of a sample size is required?
**Population Standard Deviation (σ):** 76.5
**Confidence Level:** 95%
**Margin of Error:** 1
**Hint:** For assistance, you can refer to this [Video](#).
**Formula for Sample Size (n):**
\[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \]
- Z is the z-value corresponding to the desired confidence level (for 95%, Z = 1.96)
- σ is the population standard deviation
- E is the margin of error
**Calculation:**
\[ n = \left( \frac{1.96 \cdot 76.5}{1} \right)^2 \]
Here, you need to:
1. Multiply the Z value by the population standard deviation.
2. Divide the product by the margin of error.
3. Square the result to get the sample size.
After completing the calculation, fill in the sample size in the box below:
\[ n = \boxed{} \]
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