Question

If you want to be 95​% confident of estimating the population proportion to within a sampling error of ±0.06 and there is historical evidence that the population proportion is approximately .40​, what sample size is​ needed?

Answer 1

Solution :

Given that,

= 0.40

1 - = 1 - 0.40 = 0.60

margin of error = E = % = 0.06

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )   

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

= (1.645 / 0.06)2 * 0.40 * 0.6

=180.40

Sample size = 181