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 = 36.9 . You would like to be 98% confident that your estimate is within 0.2 of the true population mean. How large of a sample size is required?

Answer 1

Solution :

Given that,

Population standard deviation = = 36.9

Margin of error = E = 0.2

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z_/2 = 2.326

sample size = n = [Z_/2* / E] ²

n = [ 2.326 * 36.9 / 0.2]²

n = 184167.14

Sample size = n = 184168