5 6 A random sample of 144 patients suffering from a partic

5 - 6. 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. 5. a) Construct a 90% (two-sided) confidence interval for the overall improvement rate of this medicine. b) Find the minimum sample size required if we want to estimate the improvement rate of this medicine to within 4% with 90% confidence if it is known that the improvement rate is between 70% and 90%. c) 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