Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99.5% confident that your esimate is within 4% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

At 99.5% confidence level the z is ,

= 1 - 99.5% = 1 - 0.995 = 0.005

/ 2 = 0.005 / 2 = 0.0025

Z_/2 = Z_0.0025 = 2.807

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

   = (2.807 / 0.04)² * 0.5 * 0.5

   = 1231

sample size = 1231