The National Highway Transportation Safety Administration runs crash tests in which stock automobiles are crashed into a wall at 35 mph with dummies in both the passenger and the driver€™s seats. The THOR Alpha crash dummy is capable of recording 134 channels of data on the impact of the crash at various sites on the dummy. In this test, 335 cars are crashed. The response variable is a measure of head injury. Researchers want to know whether the seat the dummy is sitting in affects head injury severity, as well as whether the type of car affects severity. Here are boxplots for the 2 different Seats (driver, passenger) and the 6 different Size classifications (compact, light, medium, mini, pickup, van).

An interaction plot shows:

A scatterplot of residuals vs. predicted values shows:

The ANOVA table follows:

a) State the null hypotheses about the main effects (in words, not symbols).
b) Are the conditions for two-way ANOVA met?
c) If so, perform the hypothesis tests and state your conclusion. Be sure to state it in terms of head injury severity, seats, and vehicle types.

Transcribed Image Text:

2 3.25 3.00 2.75 2.50 Driver Passenger Seat 3.0 2.7 2.4 Compact Light Medium Mini Pickup Van Size Driver Passenger 2.7 2.5 Compact Light Medium Mini Pickup Varn Size 2.9 3.0 3.1 Predicbed Values (severity index) Sum of Mean Source DF Squares Square F-ratio P-value Seat Size Seat x Size 5 0.07224 0.01445 0.415 0.838 Error Total 1 0.88713 0.88713 25.501 <0.0001 5 1.49253 0.29851 8.581 <0.0001 282 9.8101 0.03479 293 12.3853