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=75.4σ=75.4. You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required? n=____

Answer 1

Solution

standard deviation =   =75.4

Margin of error = E = 5

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96* 75.4 / 5 )2

n =873.60

Sample size = n =874 rounded