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 = 75.2 . 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?

n =

Answer 1

Solution :

Given that,

= 75.2

E = 5

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.58

Margin of error = E =( Z_/2* / E)²

  = ( 2.58 * 75.2 / 5 )²

⁼   1505.68

n =1506