Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=19%p∗=19%. You would like to be 99.5% confident that your estimate is within 0.5% 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,

= 19%=0.19

1 - = 1 - 0.19 = 0.81

margin of error = E = 0.5% = 0.005

At 99.5% confidence level the z is ,

Z/2 = 2.807( Using z table )

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

= (2.807/ 0.005)2 * 0.19 * 0.81

= 48504.65

Sample size =48505