Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 82%. You would like to be 90% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required?

n =

Answer 1

Solution,

Given that,

= 0.82

1 - = 1 - 0.82 = 0.18

margin of error = E = 0.03

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_0.05 = 1.645

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

= (1.645 / 0.03)² * 0.82 * 0.18

= 443.78

sample size = n = 444