(1 point) A random sample of elementary school children in New York state is to

Question

(1 point) A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. An interval estimate of the proportion p with a margin of error of 0.03 and 98% confidence is required (a) Assuming no prior information about p is available, approximately how large of a sample size is needed? (b) If a planning study indicates that p is around 0.8, approximately how large of a sample size is needed? n=

Explanation / Answer

Margin of error is given as z*Sqrt(p*(1-p)/N)

z for 98% confidence is 2.33

a) 0.03=2.33*sqrt(0.5*0.5/N) , we assume p=0.5 if not provided

or N is 0.5*0.5*(2.33/0.03)^2=1508.0278 or 1509

b) 0.03=2.33*sqrt(0.8*0.2/N)

or N is 0.8*0.2*(2.33/0.03)^2=965.1378 or 966

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