A study is planned to investigate

(a) whether four gasoline additives differ with respect to the reduction in oxides of nitrogen and

(b) if such differences exist whether they depend on the makes of the cars used in the study. The investigator has selected three makes (models) of cars, Ford, Honda, and Porsche. For each model he has four cars available, and he uses four different drivers. He believes that for each model systematic differences are likely to occur in the cars' performance. Also, even though the drivers may do their best to drive the car in a manner required by the test, systematic differences can occur from driver to driver. In planning the study the investigator would like to have an experimental design that eliminates the car-to-car variation and the driver-to-driver variation. He wants to use the same four drivers for the whole experiment. (i) Give the name for an appropriate experimental design. (ii) Write out the actual assignment of the additives to car-driver combinations for the three models. (iii) Give a linear model and outline the ANOVA table for this experiment, giv- ing sources of variation and d.f. (iv) Give the SAS statements (classes, model) for the model in (iii). (v) Indicate how you would use the ANOVA to investigate the questions

(a) and

(b) raised above.