Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p*=39%

. You would like to be 99.5% confident that you estimate is within 2% of the true population proportion. How large of a sample size is required?

n =

Do not round mid-calculation. However, use a critical value accurate to three decimal places.

Answer 1

Solution :

Given that,

= 0.39

1 - = 1 - 0.39 = 0.61

margin of error = E = 0.02

At 99.5% confidence level

= 1 - 99.5%

=1 - 0.995 = 0.005

/2 = 0.0025

Z/2 = 2.807

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

= (2.807 / 0.02)² * 0.39 * 0.61

= 4686.18335

= 4687