When 490 college students were surveyed 120 said they own th

When 490 college students were surveyed, 120 said they own their car. Construct a 95% confidence interval for the proportion of college students who say they own their cars.

Solution

p=120/490 =0.244898

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) = 0.244898 -1.96*sqrt(0.244898*(1-0.244898)/490) =0.2068218

So the upper bound is

p+ Z*sqrt(p*(1-p)/n) = 0.244898 +1.96*sqrt(0.244898*(1-0.244898)/490) =0.2829742