Construct a confidence interval of the population proportion

Construct a confidence interval of the population proportion at the given level of confidence.

x=105, n=150, 95% confidence

the 95% confidence interval is ______, ______ (Use asending order and round three decimal places)

Solution

p=105/150 =0.7

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) =0.627

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.7 +1.96*sqrt(0.7*0.3/150) =0.773