It is of importance to ascertain how the lengths of steel bars produced two scre
ID: 3057292 • Letter: I
Question
It is of importance to ascertain how the lengths of steel bars produced two screw machines are affected by heat treatments and the time of day the bars are produced. A factorial experiment using two machines (A and B), two heat treatments (W and L), and two times (8 am and 3 pm) was conducted. Our ultimate goal will be to determine the final prediction model.
Use significance level 0.05, based on the pvalue from the ANOVA table, answer the following questions: i. Is the three-way interaction significant? Briefly explain. ii. If you can continue after (i), are the two-way interactions significant? Briefly explain. iii. Which main effects can be tested for significance after (ii)? Briefly explain. iv. Test the significance of any main effects you can test. Briefly explain.
Means of each treatment Machine Heat Time Length 10 MP Output Response Length Analysis of Variance Model C. Total DF Sum of Squares 95.93750 25.50000 121.43750 Mean Square 13.7054 3.1875 F Ratio 4.2997 Prob > F 0.0289 15 Parameter Estimates Term Estimate 6.3125 1.6875 1.4375 0.0625 0.0625 0.9375 0.3125 0.3125 Std Error 0.446339 0.446339 0.446339 0.446339 0.446339 0.446339 0.446339 0.446339 tRatio 4.14 3.78 3.22 0.14 0.14 2.10 0.70 0.70 Prob Machine Heat Machine Heat Time Machine Time Heat' Time Machine Heat TimeExplanation / Answer
by looking at ANOVA table,
(i) The three - way interaction is not significant in nature. as p - value is greater than significance level 0.05 here so the interaction between machine, time and heat is insignificant here.
(ii0 Here there are three two - way interactions i.e. machine * heat (p - value = 0.8921) , machine * time ( p-value = 0.0689) and heat * time (p - value = 0.5037) , all the two- way interactions has p - value greater than significance level 0.05 so we can say that none of the two - way interactions significant.
(iii) Now we will check single factor significance where
(iv) The machine (has p-value = 0.0054), Heat (p - value = 0.0122) , Time (p- value = 0.8921) so we can say that time factor is insignificant here but
machine" and "heat" factors are significant here.
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