The chemical element antimony is sometimes added to tin–lead solder to replace the more expensive tin and to reduce the cost of soldering. A factorial experiment was conducted to determine how antimony affects the strength of the tin–lead solder joint (Journal of Materials Science, May 1986). Tin–lead solder specimens were prepared using one of four possible cooling methods (water-quenched, WQ; oil-quenched, OQ; air-blown, AB; and furnace-cooled, FC) and with one of four possible amounts of antimony (0%, 3%, 5%, and 10%) added to the composition. Three solder joints were randomly assigned to each of the 4 × 4 = 16 treatments and the shear strength of each measured. The experimental results, shown in the next table, were subjected to an ANOVA.

a. Construct an ANOVA summary table for the experiment.

b. Conduct a test to determine whether the two factors, amount of antimony and cooling method, interact. Use α = .01.

c. Interpret the result obtained in part b.

d. If appropriate, conduct the tests for main effects. Use α = .01.    

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ANTIMONY Amount of Antimony % weight Cooling Method Shear Strength MPa WQ 17.6, 19.5, 18.3 OQ 20.0, 24.3, 21.9 AB 18.3, 19.8, 22.9 FC 19.4, 19.8, 20.3 3 WQ 18.6, 19.5, 19.0 3 OQ 20.0, 20.9, 20.4 3 AB 21.7, 22.9, 22.1 3 FC 19.0, 20.9, 19.9 WQ OQ 5 22.3, 19.5, 20.5 20.9, 22.9, 20.6 5 AB 22.9, 19.7, 21.6 FC 19.6, 16.4, 20.5 WQ OQ 10 15.2, 17.1, 16.6 10 16.4, 19.0, 18.1 10 AB 15.8, 17.3, 17.1 10 FC 16.4, 17.6, 17.6