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%p*=39%. You would like to be 99% confident that you estimate is within 2.5% 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 = 0.025

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 * 0.39 * 0.61

= 2526

sample size = n = 2526