Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 80% confident that you estimate is within 2% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

= 1 - = 0.5

margin of error = E = 2% = 0.02

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.8 = 0.2

/ 2 = 0.2 / 2 = 0.1

Z_/2 = Z_0.1 = 1.282

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

= (1.282 / 0.02)² * 0.5 * 0.5

= 1027

sample size = 1027