Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=87%. You would like to be 99.9% confident that your esimate is within 3% of the true population proportion. How large of a sample size is required?

n =

Answer 1

Solution :

Given that,

= 0.87

1 - = 1 - 0.87 = 0.13

margin of error = E = 0.03

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 / 0.03)2 * 0.87 * 0.13

= 1361

sample size = n = 1361