Each year the National Highway Traffic Safety Administration (NHTSA) conducts crash tests for new cars. Crash-test dummies are placed in the driver’s seat and front passenger’s seat of a new-car model, and the car is steered by remote control into a head-on collision with a fixed barrier while traveling at 35 miles per hour. The results for 98 new cars are saved in the CRASH file. Two of the variables measured for each car in the data set are (1) the severity of the driver’s chest injury and (2) the severity of the passenger’s chest injury. (The more points assigned to the chest injury rating, the more severe the injury.) Suppose the NHTSA wants to determine whether the true mean driver chest injury rating exceeds the true mean passenger chest injury rating, and if so, by how much.
a. State the parameter of interest to the NHTSA.
b. Explain why the data should be analyzed as matched pairs.
c. Find a 99% confidence interval for the true difference between the mean chest injury ratings of drivers and front-seat passengers.
d. Interpret the interval, part c. Does the true mean driver chest injury rating exceed the true mean passenger chest injury rating? If so, by how much?
e. What conditions are required for the analysis to be valid? Do these conditions hold for this data?