SOLUTION: After calculating the sample size needed to estimate a population proportion to within .04, your statistics professor told you the maximum allowable error must be reduced to just .

Question 1089637: After calculating the sample size needed to estimate a population proportion to within .04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led t a sample size of 800, the sample size will now have to be:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
error = function {sqrt(p*(1-p)/n)}
error^2*n= function of p(1-p)
n=function of p(1-p)/error^2
1/4 of the error is 1/16 in the denominator and that means the sample size must be 16 times higher or 12,800.
Put in numbers to check and use alpha of 0.05
0.04=1.96*sqrt(p(1-p)/800)
0.0016*800=3.84 p(1-p)
1.28/3.84=p(1-p)=0.33
now change error to 0.01
0.0001*n=0.33*3.84=1.28
1.28/0.0001=12,800

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