A manufacturing firm produces a single product on three production lines. Because the lines were developed at different points in the firm’s history, they use different equipment. The firm is considering changing the layouts of the lines and would like to know what effects different layouts would have on production output. A study was conducted to determine the average output for each line over four randomly selected weeks using each of the three layouts under consideration. The output (in hundreds of units produced) was measured for each line for each of the four weeks for each layout being evaluated. The results of the study are as follows:

Line 1 Line 2 Line 3 Layout 1 12 12 11 10 14 10 12 10 14 12 11 12 Layout 2 17 16 18 18 15 18 15 16 17 17 17 18 Layout 3 12 10 11 12 11 11 11 11 10 11 11 12

a. Based on the sample data, can the firm conclude that there is an interaction effect between the type of layout and the production line? Conduct the appropriate test at the 0.05 level of significance.

b. At the 0.05 level of significance, can the firm conclude that there is a difference in mean output across the three production lines?

c. At the 0.05 level of significance, can the firm conclude that there is a difference in mean output due to the type of layout used?