A highway safety institution conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In the institute's 40-mph offset test, 40% of the total width of each vehicle strikes a barrier on the driver's side. The barrier's deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. You are in the market to buy a family car and you want to know if the mean head injury resulting froom this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles(SUVs). The data in the accompanying table were collected from theinstitute's study. Large Family Cars Passenger Vans Midsize Utility Vehicles
263 148 225
134 240 214
407 338 188
527 695 306
148 547 351
627 475 553
164 321 395
(a) State the null and alternative hypotheses
(b) Test the hypothesis that the mean head injury for each vehicle type is the same at the ?=0.01 level of significance.
(c) Use technology to find the F-test statistic for this data set.
(d) Determine the P-value and state the appropriate conclusion.