In an Experiment to See Whether the Amount of Coverage

Essay

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). $$\begin{array} { l l | c c c } \hline & & { \text { Roller Brand } } \\\hline & & \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } \\\text { Paint Brand } & \mathbf { 2 } & 404 & 396 & 401 \\& \mathbf { 2 } & 396 & 394 & 397 \\& \mathbf { 3 } & 389 & 392 & 394 \\& \mathbf { 4 } & 394 & 387 & 393 \\\hline\end{array}$$
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?