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 = 56.5 . You would like to be 98% confident that your esimate is within 4 of the true population mean. How large of a sample size is required?

n =

Answer 1

Solution :

Given that,

standard deviation =   =56.5

Margin of error = E = 4

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z_/2 = Z_0.01 = 2.326 ( Using z table    )

sample size = n = [Z_/2* / E] ²

n = ( 2.326* 56.5 /4 )²

n =1079.43

Sample size = n =1079