Question

If you want to be 99​% confident of estimating the population proportion to within a sampling error of ± 0.05 and there is historical evidence that the population proportion is approximately 0.37, what sample size is​ needed?

A sample size of   is needed.

​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

= 0.37

1 - = 1 - 0.37 = 0.63

margin of error = E = 0.05

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.05

Z_/2 = Z _0.005 = 2.576

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

= (2.576 / 0.05)² * 0.37 * 0.63

= 619

sample size = 619