Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 12 % p∗=12% . You would like to be 99.5% confident that your esimate is within 2% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

= 12%=0.12

1 - = 1 - 0.12 = 0.88

margin of error = E = 2% = 0.02

At 99.5% confidence level the z is ,

= 1 - 99.5% = 1 - 0.995 = 0.005

/ 2 = 0.005 / 2 = 0.0025

Z_/2 = Z_0.0025 = 2.807

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.807/ 0.02)² * 0.12 * 0.88

= 2080.12 = 2081

Sample size = 2081