Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.14. You would like to be 98% confident that your esimate is within 3% of the true population proportion. How large of a sample size is required? n=____

Answer 1

Solution :

Given that,

= 0.14

1 - = 1 - 0.14 = 0.86

margin of error = E = 3% = 0.03

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 / 0.03)2 * 0.14 * 0.86

=723.77

Sample size = 724