Planning Parenthood ®, a national organization that assiststeenage mothers with
ID: 2955265 • Letter: P
Question
Planning Parenthood ®, a national organization that assiststeenage mothers with pregnancy, estimates that approximately 37% ofthe women coming into the center had contracted a sexuallytransmitted infection. They wish to plan a study to obtain amore statistically relevant estimate.
How many samples are required if we wish a 95%confidence interval that is within 0.03 of the true populationproportion?
How many samples would be required if we wished toobtain the maximum possible number of samples needed (i.e., we donot want to rely on the 37% estimate from above) with a 95%confidence and 0.03 error?
Explanation / Answer
(1) Given p=0.37, E=0.03 =0.05, |Z(0.025)|=1.96 (check normal table) n=(Z/E)^2*p*(1-p) =(1.96/0.03)^2*0.37*(1-0.37) = 994.9744 Take n=995 (2) p=0.5 n=(Z/E)^2*p*(1-p) =(1.96/0.03)^2*0.5*(1-0.5) = 1067.111 Take n=1068