Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p?=11%. You would like to be 99.9% confident that your esimate is within 5% of the true population proportion. How large of a sample size is required?

Answer 1

Solution:

Given that,

= 0.110

1 - = 1 - 0.110 = 0.890

margin of error = E = 5% = 0.05

At 99.9% confidence level the z is ,

= 1 - 99% = 1 - 0.0999 = 0.001

/ 2 = 0.001/ 2 = 0.0005

Z_/2 = Z_0.0005 = 3.291

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

= (3.291/ 0.05)² * 0.110 * 0.890

= 424.1294

= 424

n = sample size = 424