Question

A 99% confidence interval estimate of the proportion of a population having a particular characteristic is needed. The estimate must have a margin of error of 0.025. How large must the sample size be?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.025

  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 = 2.576

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.576 / 0.025)² * 0.5 * 0.5

= 2654.3 = 2655

sample size = 2655