A random sample of 100 preschool children in Tokyo revealed

A random sample of 100 preschool children in Tokyo revealed that only 60 had been vaccinated. Provide a 90% con?dence interval for the proportion vaccinated in the city.

Solution

p=60/100=0.6

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

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.6 -1.645*sqrt(0.6*0.4/100) =0.5194118

So the upper bound is

p + Z*sqrt(p*(1-p)/n) = 0.6 +1.645*sqrt(0.6*0.4/100) =0.6805882