Question

If you want to be 95​% confident of estimating the population proportion to within a sampling error of ±0.02 and there is historical evidence that the population proportion is approximately .35​, what sample size is​ needed?

Answer 1

Solution :

Given that,

= 0.35

1 - = 1 - 0.35 = 0.65

margin of error = E = % = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

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

= (1.96 / 0.02)2 * 0.35 * 0.65

= 2184.91

Sample size = 2185