Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p*=30%p*=30%. You would like to be 99.9% confident that you estimate is within 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,

= 0.30

1 - = 1 - 0.30 = 0.70

margin of error = E = 0.05

At 99.9% confidence level

= 1 - 99.9%

= 1 - 0.999 =0.001

/2 = 0.0005

Z/2 = Z0.0005  = 3.291

sample size = n = (Z / 2 / E )2 * * (1 - )

= (3.291 / 0.05)2 * 0.30 * 0.70

= 909.77

sample size = n = 910