In: Statistics and Probability
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?
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