Question

If you want to be 99% confident of estimating the population proportion to within a sampling error of ±0.06, what sample size is​ needed?

Answer 1

Solution :

Given that,

= 1 - =0.5

margin of error = E = 0.06

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= (2.576 / 0.06)² * 0.5 * 0.5

= 460.8 = 461

sample size = 461