Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 34.5 . You would like to be 99% confident that your estimate is within 10 of the true population mean. How large of a sample size is required?

Answer 1

Required sample size is minimum 79

Explanation:

Minimum sample size to estimate the true population mean is given by the formula:

N≥
`((z*s)/(E))^(2)` where

• N is the minimum sample size to estimate the population mean
• z is the corresponding z-score for the given confidence level
• s is the sample standard deviation
• E is the margin of error of the population mean

z=2.58 for 99% confidence level, s= 34.5 and E=10. If we put these numbers in the formula:

N≥
`((2.58*34.5)/(10)) ^(2)` =78.97 ≈ 79