Gas mileage revisited. A student runs an experiment to study the effect of Tire Pressure and Acceleration on gas mileage. He devises a system so that his Jeep Wagoneer uses gasoline from a one-liter container. He uses 3 levels of Tire Pressure (low, medium, and full) and 2 levels of Acceleration, either holding the pedal steady or pumping it every few seconds. He randomizes the trials, performing 4 runs under each treatment condition, carefully recording the number of miles he can go in his Jeep Wagoneer on one liter of gas.
a) What are the null and alternative hypotheses for the main effects?
b) How many degrees of freedom does each treatment sum of squares have? How about the error sum of squares?
c) Should he consider fitting an interaction term to the model? Why might it be a good idea?
d) If he fits an interaction term, how many degrees of freedom would it have?