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?

Question

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?

Quizplus · Accepted Answer

The Answer of 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?

In an Experiment to See Whether the Amount of Coverage