The Kingston Review KR is testing a new GMAT question The KR

The Kingston Review (KR) is testing a new GMAT question. The KR wants to determine what proportion of test-takers will answer the question correctly, in order to assess its difficulty. In a random sample of 150 test-takers, 70% answered the question correctly. What is the 95% confidence interval for the proportion of test-takers answering the question correctly?

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.7 -1.96*sqrt(0.7*0.3/150) =0.6266635

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.7 +1.96*sqrt(0.7*0.3/150) =0.7733365