"Better brakes make safer cars, and manufacturers compete to have the best. To keep this competition honest, the Department Of Transportation (DOT) occasionally tests cars to see that safety features perform as adver- tised. Rather than rely on testing done by manufacturers or Consumers Union, DOT acquires cars such as the Toyota Camry and tests them itself.
For this experiment, the DOT measures the topping distance for a sample of 50 Camrys. The data is in the Minitab file dist stop.mtw. All 50 stops were done under carefully monitored, near identical conditions. Each car was going 50 miles per hour. Each time the driver stopped on a patch of wet pavement. The same driver performed every test, the technicians checked the road to ensure that the conditions remained the same.
(a) A competitors model takes 180 feet under these conditions to stop from 50 miles per hour. How can Toyota use these results to its advantage?(You do not need to do any statistical calculations).
(b) As a driver, would you rather have a 95% confidence interval for the mean stopping distance or a 80% CI as its margin of error would be lesser. Justify.
(c) Why does the DOT have the same driver at the wheel for the entire test? (d) Do the data meet the conditions necessary for a t-interval for the mean stopping distance?
(e) Construct a two sided 95% confidence interval for the mean stopping distance. Interpret the interval. (f) Test the null hypothesis H0 : μ ≥ 180 against an appropriate alternative at the 5% level.
(g) On the basis of these calculations, can Toyota advertise that its cars stop in less than 180 feet under these conditions?