Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 25%. You would like to be 98% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?

n =

Answer 1

Solution :

Given that,

= 0.25

1 - = 1 - 0. 25= 0.75

margin of error = E = 3.5% = 0.035

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z_/2 = 2.326 ( Using z table )

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

= (2.326 / 0.035)² * 0.25 * 0.75

=828.10

Sample size = 828