The output of a continuous extruding machine that coats steel pipe with plastic

Question

The output of a continuous extruding machine that coats steel pipe with plastic was studied as a function of the thermostat temperature profile (A, at three levels), the type of plastic (B, at three levels), and the speed of the rotating screw that forces the plastic through a tube-forming die (C, at three levels). There were two replications (L 2) at each combination of levels of the factors, yielding a total of 54 observations on output. The sums of squares were SSA = 14,124.44, SSB 5521.27, SSC 244,696.39, SSAB 1049.62, SSAC 67.67, SSBC 336.67, SSE = 3128.5, and SST- 270,024.33 (a) Construct the ANOVA table. (Round your answers to two decimal places.) Source df MS AB AC BC ABC Error Total (b) Use appropriate F tests to show that none of the F ratios for two- or three-factor interactions is significant at level 0.05 by finding the critical value for each test. (Round your answers to two decimal places.) Source F AB BC AC ABC 0.05 (c) Which main effects appear significant? (Select all that apply.) O A (thermostat temperature profile) B (type of plastic) O C (speed of the rotating screw) O No main effects are significant at level 0.05 (d) with x1-= 8262, x,-2-97 12, and x3. = 11,210, use Tukey's procedure to identify significant differences, at a level 0.05 among the levels of factor C. (Round the degrees of freedom down to the nearest value available in the appropriate table.) Which means differ significantly? (Select all that apply.) x and x x and x x and x .2 ,3 ,3 O There are no significant differences

Explanation / Answer

b)

F.inv.rt(0.05,df ,df_error)

c)

F > F_critical , then variable is signiifcant

here A, B, C are significant

hence

first three options are all correct

. The speed of the rotating screw, the type of plastic, and the thermostat temperature are significant

d)

all three are different from each other

SS df MS f f-CRITICAL A 14124.44 2 7062.22 60.94931756 3.354130829 B 5521.27 2 2760.635 23.82520217 3.354130829 C 244696.4 2 122348.195 1055.90579 3.354130829 AB 1049.62 4 262.405 2.2646428 2.727765306 AC 67.67 4 16.9175 0.146003676 2.727765306 BC 336.67 4 84.1675 0.726393639 2.727765306 ABC 1099.77 8 137.47125 1.186422806 2.305313177 ERROR 3128.5 27 115.8703704 270024.3 53

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