The Super Metals company is evaluating the procedure that allows to minimize the manufacturing times (minutes) to achieve the desired finish of the pieces, therefore, they hire you as a consultant in the area of design of experiments and they ask you to provide a proposal that allows to optimize the process. The factors of interest in the study are A - the material used as a support for the part process, which can be Pewter, Stainless Steel or Copper; B - the temperature to which the part is subjected, which is based on three levels, that is, low, medium or high temperature; and C - the glue application method which can be by brush or expected. The experiment is carried out and then the results obtained:

a) State the hypothesis test b) Carry out the corresponding Simplified ANOVA Table with a significance level of 5% and issue conclusions ( c) Determine the% variation that is explained with this model d) Of the significant factors, determine in what percentage they explain the behavior of the response variable and define which factors are the most important to control. e) For the main factors (A, B and C) make an effects graph with a 95% confidence interval and draw conclusions. f) Make the simple effects graph for the double interaction factors that have been significant in the model. g) Apply the LSD test for the following comparison: to. A - Pewter with C - VS Brush A - Pewter with C - Sprayed h) Provides a recommendation that allows minimizing the manufacturing time of the part.

PELTRE T. Baja T. Media 21.1 6.8 20.32 T. Alta 5 4.52 ACERO INOXIDABLE T. Baja T. Media T. Alta 20.58 5.49 5.27 4.55 COBRE T. Media 15.26 17.49 15.1 T. Alta 13.4 T. Baja 31.07 34.5 33.3 14.26 Brocha 16.06 21.47 6.42 5.22 21.16 4.12 14.36 5.39 5.27 7.44 5.37 3.56 7.5 4.11 12.56 11.23 Espreado 7.12 4.45 3.39 7.07 4.01 3.24 15.28 11.52 10.14 7.38 5.58 4.38 7.21 5.16 4.42 14.55 13.04 10.55 PELTRE T. Baja T. Media 21.1 6.8 20.32 T. Alta 5 4.52 ACERO INOXIDABLE T. Baja T. Media T. Alta 20.58 5.49 5.27 4.55 COBRE T. Media 15.26 17.49 15.1 T. Alta 13.4 T. Baja 31.07 34.5 33.3 14.26 Brocha 16.06 21.47 6.42 5.22 21.16 4.12 14.36 5.39 5.27 7.44 5.37 3.56 7.5 4.11 12.56 11.23 Espreado 7.12 4.45 3.39 7.07 4.01 3.24 15.28 11.52 10.14 7.38 5.58 4.38 7.21 5.16 4.42 14.55 13.04 10.55