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

Answer 1

n = 400

Explanation:

The formula for the error in our estimate is given by:Standard Error : √ ( p(1-p)/ n)Error = SE = Zα/2 √ ( p(1-p)/ n) where Zα/2= critical value for 95% confidence level = 1.96and we know our error is 3.5 %But we do not the sample proportion p. Then what we can do is give an estimate of p in the absence of any other information.In this case we will use p= 0.5 which is the value that maximizes the expression for the standard error :if p = 0.8 then SE= 0.040 p = 0.3 then SE =0.036 p = 0.1 then SE = 0.030 p = 0.5 then SE = 0.050Substituting3.5/100 = 1.96 x √ (( 0.5 x 0.5 ) /n )3.5/ (100 x 1.96 x 0.5 ) = 1/ √n0.0357 = 1 /√n n = 20²