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 1 channel 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 if which seat the dummy is in affects head injury severity, as well as whether the type of car affects severity.
Here are partial box plots for the 2 different Seats (driver, passenger) and the 6 different Size classifications (compact, light, medium, mini, pickup, van):

An interaction plot shows:

A scatter plot of residuals vs. predicted values shows:

a) Are the conditions for two-way ANOVA met?
b) State the hypotheses about the main effects (both numerically and in words).
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:

3.25 3.00 2.75 2.50 Driver Passenger Seat 3.3 3.0 2.7 st申申申 고 보 Compact Light Medium Mini Pickup Van Size 3.5 3.3 2.9 Passenger 2.5 2.3 2.1 Compact Light Medium Mini Pickup Van Size 0.6T. 0.3 0.3T 3.1 2.9 3.0 2.8 Predicted Values (severity index) The ANOVA table follows: Analysis of Variance for Head Severity: 293 cases Sum of Mean DF Squares Square F-ratio P-value Source Seat 1 0.88713 0.88713 25.501 <0.0001 5 1.49253 0.2985 8.581 <0.0001 Size Seat X Size 5 0.07224 0.01445 0415 0.838 Error Total 282 9.8101 0.03479 293 12.3853