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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?

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Answer:

Required sample size is minimum 79

Step-by-step explanation:

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

N≥[tex](\frac{z*s}{E})^{2}[/tex] 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≥[tex](\frac{2.58*34.5}{10}) ^{2}[/tex] =78.97 ≈ 79

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