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 = 75.1 . You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.

n =

Answer 1

Solution :

Given that,

standard deviation =   =75.1

Margin of error = E = 1

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = 2.576  

sample size = n = [Z_/2* / E] ²

n = ( 2.576* 75.1 / 1 )²

n =37426

Sample size = n =37426