Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately ˆp=63%p^=63%. You would like to be 95% confident that your esimate is within 3% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

= 63%=0.63

1 - = 1 - 0.63= 0.37

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 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

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

= (1.96 / 0.03)2 * 0.63 * 0.37

= 995

Sample size = 995