Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 57%. You would like to be 98% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required?

n =

Answer 1

Solution :

Given that,

= 0.57

1 - = 1 - 0.57 = 0.43

margin of error = E = 0.045

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z/2 = Z 0.01 = 2.326

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

= (2.326 / 0.045)2 * 0.57 * 0.43

= 655

sample size = n = 655