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 99% confident that your esimate is within 2.5% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

= 0.14

1 - = 1 - 0.14= 0.86

margin of error = E = 2.5% = 0.025

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.025)2 * 0.14* 0.86

=1278.31

Sample size =1278 rounded