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=72.7. You would like to be 99% confident that your esimate is within 3 of the true population mean. How large of a sample size is required?

n =

Answer 1

Given that,

standard deviation =s =   =72.7

Margin of error = E = 3

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* 72.7/ 3 )2

n =3896.888

Sample size = n =3897