Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.43. You would like to be 95% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

= 0.43

1 - = 1 - 0.43 = 0.57

margin of error = E = 1.5% = 0.015

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= (1.96 / 0.015)2 * 0.43* 0.57

= 4184.78

Sample size =4185 rounded