29. The article “An Analysis of Variance Applied to Screw Machines” (Industrial Quality Control, 1956: 8–9) describes an experiment to investigate how the length of steel bars was affected by time of day (A), heat treatment applied (B), and screw machine used (C). The three times were 8:00 A.M., 11:00 A.M., and 3:00 P.M., and there were two treatments and four machines (a 3  2  4 factorial experiment), resulting in the accompanying data [coded as 1000(length  4.380), which does not affect the analysis].

B1 C1 C2 C3 C4 A1 6, 9, 7, 9, 1, 2, 6, 6, 1, 3 5, 5 0, 4 7, 3 A2 6, 3, 8, 7, 3, 2, 7, 9, 1, 1 4, 8 1, 0 11, 6 A3 5, 4, 10, 11, 1, 2, 10, 5, 9, 6 6, 4 6, 1 4, 8 B2 C1 C2 C3 C4 A1 4, 6, 6, 5, 1, 0, 4, 5, 0, 1 3, 4 0, 1 5, 4 A2 3, 1, 6, 4, 2, 0, 9, 4, 1, 2 1, 3 1, 1 6, 3 A3 6, 0, 8, 7, 0, 2, 4, 3, 3, 7 10, 0 4, 4 7, 0 Sums of squares include SSAB
1.646, SSAC
71.021, SSBC
1.542, SSE
447.500, and SST
1037.833.

a. Construct the ANOVA table for this data.

b. Test to see whether any of the interaction effects are significant at level .05.

c. Test to see whether any of the main effects are significant at level .05 (i.e., H0A versus HaA, etc.).

d. Use Tukey’s procedure to investigate significant differences among the four machines.