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. You would like to be 98% confident that you esimate is within 0.5% of the true population proportion. How large of a sample size is required?

n =

Answer 1

Solution :

Given that,

= 0.5 ( WHEN estimate is not given than use 0.5)

1 - = 1 - 0.5= 0.5

margin of error = E = 0.5% = 0.005

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.05

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= (2.326 / 0.005)² * 0.5 * 0.5

= 54103

Sample size = 54103