Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 39 % . You would like to be 90% confident that your estimate is within 2% of the true population proportion. How large of a sample size is required?

How would I get this and where can I find a correct chart to base my z-table numbers off of to help me solve this easier?

Answer 1

Solution :

Given that,

= 0.39

1 - = 1 - 0.39 = 0.61

margin of error = E = 2% = 0.02

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645 ( using  standard normal z table)}

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

= (1.645 / 0.02)² * 0.39 * 0.61

=1609

Sample size = 1609