1. Based on a pilot study, the population standard deviation of scores for U.S. highschool graduates
taking a new version of an aptitude test has been estimated as 3.7 points. If a larger study is to be
undertaken, how large simple random sample will be necessary to have a 99% confidence that
the sample mean will not differ from the actual popultion mean by more than 1.0 point?
Solution
Given a=0.01, |Z(0.005)|=2.58 (check standard normal table) E=1, s=3.7 So
n=(Z*s/E)^2 =(2.58*3.7/1)^2 =91.12612 Take n=92