An enviornmental agency worries that many cars may be violat

An enviornmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate the percentage with a margin of error of 3% and 99% confidence. To gauge the size of the problem, the agency first picks 60 cars and finds 12 with faulty emissions systems. How many should be sampled for a full investigation?

Solution

An enviornmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate the percentage with a margin of error of 3% and 99% confidence. To gauge the size of the problem, the agency first picks 60 cars and finds 12 with faulty emissions systems. How many should be sampled for a full investigation?

P=12/60=0.2

For 99%, z=2.576

error of 3%, d=0.03

Sample size = (z²*p*(1-p))/d²

= (2.576²*0.2*0.8)/0.03²

=1179.69

The sample size required= 1180