Please I want someone to redo it clearly \"step by step\" The factors that influ

Question

Please I want someone to redo it clearly "step by step"

The factors that influence the breaking strength of a synthetic fiber are being studied Two factors are to be investigated, production machine and operator Four machines and three operators are chosen and a factorial experiment is run using fiber from the same production batch. The resulting data and Minitab output arc given on pages 11-12. including the ANOVA, associated plots, and associated Tukcy's Groupings Based on the information given, how many main effects are there in this problem? Based on the ANOVA, are the interaction effects significant at a 5% significance level? (Identify evidence to support your answer.) Which effects should be interpreted? (Circle one) main effects or interaction effects Based on the information given, which operator and which machine would you recommend given that the manufacturer is interested in maximizing breaking strength for the current customer. Briefly explain and identify the information on which you base your conclusions. Operator Number = 3 Machine Number = 4 Evidence: Analysis of variance for strength Main effects plot - means for strength Grouping information using Turkey Method and 95.0% Confidence

Explanation / Answer

Answers

Part (a)

There are two main effects – namely, machine effect and operator effect.

Part (b)

Referring to the ANOVA Table, 4th row (operator*machine, i.e., Interaction), the F-value = 2.44. This is the calculated value of F. This F has F-Distribution with degrees of freedom 6 and 16. Upper 5% point of F-Distribution with degrees of freedom 6 and 16 is 2.364 which is less than 2.44, albeit marginally. So, we say the interaction effect is significant at 5% level of significance. The same inference can also be made using the p-value given in the last column. The figure given there is 0.044 which is less than 0.05 and hence interaction effect is significant.

Part (c)

Since interaction effect is also found to be significant, for interpretational decision, that should be considered.

Part (d)

Here again, what is to be considered for decision is not the main effects, but the interaction effect since it is found to be significant. Referring to the post-hoc Tuckey Method results on interaction (last table), mean is maximum for machine4 – operator3 combination. So, our choice would be Machine 4 and Operator 3.

[Not very important, but just a ppoint of clarity – in ANOVA table, p-value against operator is given as 000. The actual value is 2.09E-13]

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