Exam 11: Multifactor Analysis of Variance

In the fixed effects model with interaction, assume that there are 4 levels of factor A, 3 levels of factor B, and 3 observations for each of the 12 combinations of levels of the two factors. Then, the number of degrees of freedom for the error sum of squares (SSE) is

In an experiment to see whether the amount of coverage of light-blue interior paint depends either on the brand of paint or on the brand of roller used, 1 gallon of each of four brands of paint was applied using each of three brands of roller, resulting in the following data (number of square feet covered). Roller Brand Paint Brand 404 396 401 396 394 397 389 392 394 394 387 393 a. Construct the ANOVA table. b. State and test hypotheses appropriate for deciding whether paint has any effect on coverage. Use $\alpha - .05$ c. Repeat part (b) for brand of roller. d. Use Tukey's method to identify significant differences among brands. Is there one brand that seems clearly preferable to the others?