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(URGENT)A Materials Engineer conducted an experiment to investigate the effect of Tempering Medium (Medium) and Material Alloy (Alloy) on the Hardness of the part. Three Tempering Media (oil, water and brine) and three Alloys (a, b and c) were used. After performing the statistical analysis, with a significance of 5%, the following results were obtained with Minitab.

a) Write the hypotheses to be tested, H0 and Ha, (you can do it in a symbolic or verbalized way). (10 points) b) Use the graphical representation of a Fisher distribution to explain the relationship between the F0, the pvalue and for the interaction between the Medium and the Alloy and with the help of this graph argues what would be the decision to take regarding the Hypothesis corresponding to this interaction. (10 points) c) Using the data presented in the ANOVA, argue if you consider that there are more factors that could significantly affect hardness. (10 points)

Pvalue Two-way ANOVA: Dureza versus Medio de Temple y Aleacin Source DF SS MS Fo Medio 2 10739.9 5369.93 67.25 Aleacin 2 4484.5 2242.26 28.08 Interaccin 4 772.1 193.04 2.42 Error 18 1437.3 79.85 Total 26 17433.9 S = 8.936 R2 = 91.76% R2 (adi) = 88.09% 0.001 0.002 0.096 Pvalue Two-way ANOVA: Dureza versus Medio de Temple y Aleacin Source DF SS MS Fo Medio 2 10739.9 5369.93 67.25 Aleacin 2 4484.5 2242.26 28.08 Interaccin 4 772.1 193.04 2.42 Error 18 1437.3 79.85 Total 26 17433.9 S = 8.936 R2 = 91.76% R2 (adi) = 88.09% 0.001 0.002 0.096

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