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=43.8σ=43.8. You would like to be 98% 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 =   =43.8

Margin of error = E = 5

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

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

n = ( 2.326*43.8 / 5 )2

n =415.17

Sample size = n =415 rounded