Question

If you want to be 95?% confident of estimating the population proportion to within a sampling error of plus or minus0.05 and there is historical evidence that the population proportion is approximately 0.38?, what sample size is? needed?

Answer 1

Solution :

Given that,

= 0.38

1 - = 1 - 0.38 = 0.62

E = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.05)² * 0.38 * 0.62

= 362.03 = 363

Sample size = n = 363