A random sample of 144 patients suffering from a particular

A random sample of 144 patients, suffering from a particular disease are given a new medicine. 108 of the patients report an improvement in their condition.

Find the minimum sample size required if we want to estimate the improvement rate of this medicine to within 4% with 90% confidence if we do not make any assumptions about the improvement rate.

Solution

p=108/144 =0.75

Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(1.645/0.04)^2*0.75*0.25

=317.1123

Take n=318