Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ? = 80 % . You would like to be 99.9% confident that your esimate is within 2.5% of the true population proportion. How large of a sample size is required?

Answer 1

Solution:

Given that,

= 0.80

1 - = 1 - 0.80 = 0.20

margin of error = E = 2.5% = 0.025

At 99.9% confidence level the z is ,

= 1 - 99.9% = 1 - 0.999 = 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 / 0.025)² * 0.80 * 0.20

= 2772.65

= 2773

n = sample size = 2773