Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data for new cars saved in the CRASH file. In Exercise 7.54. you compared the chest injury ratings of drivers and front-seat passengers using the Student’s T procedure for matched pairs. Suppose you want to make the comparison for only those cars that have a driver’s star rating of five stars (the highest rating). The data for these 18 cars are listed in the table. Now consider analyzing these data using the Wilcoxon signed ranks test.

a. State the null and alternative hypothesis.

b. Use a statistical software package to find the signed ranks test statistic.

c. Give the rejection region for the test using α = .01.

d. State the conclusion in practical terms. Report the p-value of the test.

Data from Exercise 7.54

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.

Transcribed Image Text:

CRASH5 Chest Injury Rating Driver Chest Injury Rating Driver Car Passenger Car Passenger 1 42 35 10 36 37 42 35 11 36 37 3 34 45 12 43 58 4 34 45 13 40 42 5 45 45 14 43 58 6. 40 42 15 37 41 7 42 46 16 37 41 8 43 58 17 44 57 9 9 45 43 18 42 42