Find the minimum sample size n needed to estimate μ for the given values of c, o, and E. c= 0.98, o = 6.2, and E = 1 Assume that a preliminary sample has at least 30 members. n= (Round up to the nearest whole number.)
Find the minimum sample size n needed to estimate μ for the given values of c, o, and E. c= 0.98, o = 6.2, and E = 1 Assume that a preliminary sample has at least 30 members. n= (Round up to the nearest whole number.)
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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![**Estimating Minimum Sample Size for Population Mean (μ)**
To determine the minimum sample size \( n \) needed to estimate the population mean \( \mu \), given specific values for confidence level, standard deviation, and margin of error, we will use the following parameters:
- **Confidence Level (c):** 0.98
- **Standard Deviation (\(\sigma\)):** 6.2
- **Margin of Error (E):** 1
A preliminary sample should consist of at least 30 members to ensure a reliable estimate.
**Calculation Requirement:**
The formula to calculate the minimum sample size \( n \) is:
\[ n = \left( \frac{Z_{\alpha/2} \cdot \sigma}{E} \right)^2 \]
Where:
- \( Z_{\alpha/2} \) is the Z-score associated with the desired confidence level (c).
- \(\sigma\) is the population standard deviation.
- \( E \) is the maximum error allowed, known as the margin of error.
**Instruction:**
- Compute \( n \) using the above formula and round up to the nearest whole number.
(Round up to the nearest whole number.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94c26d4c-723d-4676-abd5-06f208e5c3e0%2F59c7a882-0eb2-41ce-b2a5-1515ec8d17f0%2Fio9gip9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Estimating Minimum Sample Size for Population Mean (μ)**
To determine the minimum sample size \( n \) needed to estimate the population mean \( \mu \), given specific values for confidence level, standard deviation, and margin of error, we will use the following parameters:
- **Confidence Level (c):** 0.98
- **Standard Deviation (\(\sigma\)):** 6.2
- **Margin of Error (E):** 1
A preliminary sample should consist of at least 30 members to ensure a reliable estimate.
**Calculation Requirement:**
The formula to calculate the minimum sample size \( n \) is:
\[ n = \left( \frac{Z_{\alpha/2} \cdot \sigma}{E} \right)^2 \]
Where:
- \( Z_{\alpha/2} \) is the Z-score associated with the desired confidence level (c).
- \(\sigma\) is the population standard deviation.
- \( E \) is the maximum error allowed, known as the margin of error.
**Instruction:**
- Compute \( n \) using the above formula and round up to the nearest whole number.
(Round up to the nearest whole number.)
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