Problem 3 - Fabric experiment (30 points) The quality control department of a fabric finishing plant is studying the effect of several factors on the dyeing of cotton-synthetic cloth used to manufacture men's shirts. Three operators, three cycle times, and two temperatures were selected, and three small specimens of cloth were dyed under each set of conditions. The finished cloth was compared to a standard, and a numerical score was assigned. The data from this experiment is provided on Carmen. [Note that it is possible for an experiment to have only one replication) Temperature Cycle Time 3 1 23 24 25 300C Operator 2 27 28 26 3 31 32 29 1 24 23 28 350C Operator 2 38 36 35 40 34 36 39 50 36 35 36 34 38 39 33 34 35 37 39 35 34 38 36 34 36 31 60 28 24 27 35 35 34 26 27 25 26 29 25 36 37 34 28 26 24 a) [10 points) Write down the full (saturated) ANOVA model for this application and interpret each model component in words in the context of the application. Please be sure to include all model assumptions, and specify the numerical values of all the indexes. b) [10 points) Produce a multi-way ANOVA table in JMP (include this in your submission). Write down the ANOVA model suggested by this analysis (at significance level 0.05), including all assumptions and interpret all the terms in the model in the context of the applied problem. c) [10 points) Model diagnostics are conducted in the same way for multi-way ANOVA as for one-way ANOVA. Produce the following plots using JMP and state whether they any evidence of deviations from the ANOVA model (and, if so, state which ones) i. Residuals versus Operator levels ii. Residuals versus Cycle Time levels iii. Residuals versus Temperature levels iv. Residuals versus Predicted suggest Problem 3 - Fabric experiment (30 points) The quality control department of a fabric finishing plant is studying the effect of several factors on the dyeing of cotton-synthetic cloth used to manufacture men's shirts. Three operators, three cycle times, and two temperatures were selected, and three small specimens of cloth were dyed under each set of conditions. The finished cloth was compared to a standard, and a numerical score was assigned. The data from this experiment is provided on Carmen. [Note that it is possible for an experiment to have only one replication) Temperature Cycle Time 3 1 23 24 25 300C Operator 2 27 28 26 3 31 32 29 1 24 23 28 350C Operator 2 38 36 35 40 34 36 39 50 36 35 36 34 38 39 33 34 35 37 39 35 34 38 36 34 36 31 60 28 24 27 35 35 34 26 27 25 26 29 25 36 37 34 28 26 24 a) [10 points) Write down the full (saturated) ANOVA model for this application and interpret each model component in words in the context of the application. Please be sure to include all model assumptions, and specify the numerical values of all the indexes. b) [10 points) Produce a multi-way ANOVA table in JMP (include this in your submission). Write down the ANOVA model suggested by this analysis (at significance level 0.05), including all assumptions and interpret all the terms in the model in the context of the applied problem. c) [10 points) Model diagnostics are conducted in the same way for multi-way ANOVA as for one-way ANOVA. Produce the following plots using JMP and state whether they any evidence of deviations from the ANOVA model (and, if so, state which ones) i. Residuals versus Operator levels ii. Residuals versus Cycle Time levels iii. Residuals versus Temperature levels iv. Residuals versus Predicted suggest