Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. Your would like to be 99.9% confident that you estimate is within 1.5% 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,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 1.5% = 0.015

At 99.9% confidence level the z is ,

  = 1 - 99.9% = 1 - 0.999 = 0.001

/ 2 = 0.001 / 2 = 0.0005

Z/2 = Z0.0005 = 3.290

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

= (3.290 / 0.015)2 * 0.5 * 0.5

= 12030.63

= 12031

n = sample size = 12031