Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 23%. You would like to be 95% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

p = 23% = 0.23

1 - p = 1 - 0.23 = 0.77

margin of error = E = 3.5% = 0.035

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

sample size = n = (Z _{/ 2} / E )² * p * (1 - p)

= (1.96 / 0.035)² * 0.23 * 0.77

= 555.38 = 556

sample size = 556