Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=23%p∗=23%. You would like to be 95% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required?

n =

Do not round mid-calculation. However, use a critical value accurate to three decimal places.

Answer 1

Solution :

Given that,

= 0.23

1 - = 1 - 0.23 = 0.77

margin of error = E = 3% = 0.03

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 ( Using z table )

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

= (1.96 / 0.03)² * 0.23 * 0.77

= 756

Sample size = 756