In a metallurgy experiment, it is desired to test the eect

Chapter 15, Problem 15.3

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In a metallurgy experiment, it is desired to test the eect of four factors and their interactions on the concentration (percent by weight) of a particular phosphorus compound in casting material. The variables are A, percent phosphorus in the renement; B, percent remelted material; C, uxing time; and D, holding time. The four factors are varied in a 24 factorial experiment with two castings taken at each factor combination. The 32 castings were made in random order. The following table shows the data and an ANOVA table is given in Figure 15.8 on page 610. Discuss the eects of the factors and their interactions on the concentration of the phosphorus compound. Weight Treatment % of Phosphorus Compound Combination Rep 1 Rep 2 Total (1) 30.3 28.6 58.9 a 28.5 31.4 59.9 b 24.5 25.6 50.1 ab 25.9 27.2 53.1 c 24.8 23.4 48.2 ac 26.9 23.8 50.7 bc 24.8 27.8 52.6 abc 22.2 24.9 47.1 d 31.7 33.5 65.2 ad 24.6 26.2 50.8 bd 27.6 30.6 58.2 abd 26.3 27.8 54.1 cd 29.9 27.7 57.6 acd 26.8 24.2 51.0 bcd 26.4 24.9 51.3 abcd 26.9 29.3 56.2 Total 428.1 436.9 865.0