4M Stopping Distances
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 advertised. Rather than rely on testing done by manufacturers or Consumers Union, DOT buys cars such as the Toyota Camry described in this example and tests them itself.
For this experiment, DOT measured the stopping distance for a small sample of 10 Camrys. All 10 stops were done under carefully monitored, nearly 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, and technicians checked the road to ensure that the conditions remained the same. On average, the stops required 176 feet. With 450,000 Camrys sold each year, these 10 are a small sample.
Motivation
(a) A competitor’s model takes 180 feet under these conditions to stop from 50 miles per hour. How can Toyota use these results to its advantage?
(b) As a driver, would you rather have a 95% confidence interval for the mean stopping distance or a 95% prediction interval for the actual distance in your next emergency stop? Why?
Method
(c) What is the consequence of having the same driver at the wheel in the DOT testing?
(d) Do these data meet the conditions necessary for a t-interval for the mean stopping distance? Explain.
(e) On the basis of the distribution of these stopping distances, will inferences about the mean resemble inferences about the median in the population? Explain.
Mechanics
(f) Compute the 97.8% confidence interval for the mean and compare it with the corresponding 97.8% confidence interval for the median.
(g) Test the null hypothesis
as appropriate for these data.
Mechanics
(h) On the basis of these data, can Toyota advertise that its cars stop in less than 180 feet under these conditions? Explain your answer.