Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 90% confident that you estimate is within 4% of the true population proportion. How large of a sample size is required? n= ____

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 4% = 0.04

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.04)2 * 0.5 * 0.5

=422.816

Sample size = 423