Question

A random sample of elementary school children in New York state is to be selected to estimate the proportion ? who have received a medical examination during the past year. An interval estimate of the proportion ? with a bound of 0.035 and 98% confidence is required.

(a) Assuming no prior information about ?p is available, approximately how large of a sample size is needed?

n=

(b) If a planning study indicates that ?p is around 0.40.4, approximately how large of a sample size is needed?

n=

Answer 1

Given : Significance level=

Margin of error=E=0.035

Now , ; From standard normal distribution table

(a) SInce , the no prior information about p is available.

Therefore , assume that p=q=0.5

Therefore , the require sample saize is ,

(b) Since , p=0.40 , q=1-p=0.60

Therefore , the require sample saize is ,