A small builder of speculative homes builds three basic house designs and employs two foremen. The builder has used each foreman to build two houses of each design and has obtained the profits given in Table 11.17 (the profits are given in thousands of dollars). Figure 11.16 presents the MINITAB output of a two-way ANOVA of the house profitability data.
FIGURE 11.16
MINITAB Output of a Two-Way ANOVA of the House Profitability Data

TABLE 11.17
Results of the House Profitability Study HouseProf

a. Interpret the MINITAB interaction plot in Figure 11.16. Then test for interaction with α = .05. Can we (separately) test for the significance of house design and foreman effects? Explain why or why not.
b. Which house design/foreman combination gets the highest profit? When we analyze the six house design/foreman combinations using one-way ANOVA, we obtain MSE = .390. Compute a 95 percent (individual) confidence interval for mean profit when the best house design/foreman combination is employed.

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Rows: Poreman Columns: Design Boxplot of Profit vs Foremarn Boxplot of Profit vs Design 20 f 20 C A1l 10.65 11.95 18.80 13.80 10.25 11.80 13.15 11.73 A1l 10.45 11.88 15.98 12.77 g 15 e 15 10 1o Cell Contents: Profit : Mean Foreman Design Two-way ANOVA: Profit versus Foreman, Design Interaction Plot (data means) for Profit Source Foreman Design Interaction 2 19.292 9.6458 24.73 0.001 Error Total DE MS 20 1 12.813 12.8133 32.85 0.001 2 65.822 32.9108 84.39 0.000 Foreman 6 2.340 .3900 15 11 100.267 Foreman Design Mean 10.450 11.875 15.975 10 Mean 13.8000 11.7333 Design House Design Foremarn 10.2 11.1 9.7 10.8 12.2 11.7 11.6 12.0 19.4 18.2 13.6 12.7