Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 95% confident that you estimate is within 1.5% of the true population proportion. How large of a sample size is required?

n =

Answer 1

Solution :

Given that,

you have no preliminary estimation for the population proportion

= 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = 1.5% = 0.015

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 ( 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 / 0.015)² * 0.5* 0.5

= 4268.44444

Sample size = 4268 ROUNDED)

sample size is required