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 = 42.2 . You would like to be 99% confident that your estimate is within 5 of the true population mean. How large of a sample size is required?

Answer 1

Solution :

Given that,

standard deviation =   =42.2

Margin of error = E = 5

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58

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

n = ( 2.58* 42.5 / 5 )2

n =474.15

Sample size = n =474 rounded