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Assignment_Solution_Chp._13

# Assignment_Solution_Chp._13 - Chapter 13 Solutions 13.1 A...

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1 Chapter 13 – Solutions 13.1. A textile mill has a large number of looms. Each loom is supposed to provide the same output of cloth per minute. To investigate this assumption, five looms are chosen at random and their output is noted at different times. The following data are obtained: Loom Output (lb/min) 1 14.0 14.1 14.2 14.0 14.1 2 13.9 13.8 13.9 14.0 14.0 3 14.1 14.2 14.1 14.0 13.9 4 13.6 13.8 14.0 13.9 13.7 5 13.8 13.6 13.9 13.8 14.0 (a) Explain why this is a random effects experiment. Are the looms equal in output? Use α = 0.05. The looms used in the experiment are a random sample of all the looms in the manufacturing area. The following is the analysis of variance for the data: Minitab Output ANOVA: Output versus Loom Factor Type Levels Values Loom random 5 1 2 3 4 5 Analysis of Variance for Output Source DF SS MS F P Loom 4 0.34160 0.08540 5.77 0.003 Error 20 0.29600 0.01480 Total 24 0.63760 Source Variance Error Expected Mean Square for Each Term component term (using restricted model) 1 Loom 0.01412 2 (2) + 5(1) 2 Error 0.01480 (2) (b) Estimate the variability between looms. 01412 0 5 0148 0 0854 0 2 . . . n MS MS ˆ E Model = - = - = τ σ (c) Estimate the experimental error variance. 0148 0 2 . MS ˆ E = = σ (d) Find a 95 percent confidence interval for ( ) 2 2 2 σ σ σ τ τ + .

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2 2, 1, 1 1 1 0.08540 1 1 1 0.1288 5 0.01480 3.51 Model E a n a MS L n MS F α - - = - = × - = 1 2, 1, 2 2 2 2 2 2 1 1 1 0.08540 1 8.56 1 9.6787 5 0.01480 1 1 0.1141 0.9064 Model E a n a MS U n MS F L U L U α τ τ τ τ σ σ σ σ σ σ - - - = - = × - = + + + + (e) Analyze the residuals from this experiment. Do you think that the analysis of variance assumptions are satisfied? There is nothing unusual about the residual plots; therefore, the analysis of variance assumptions are satisfied. 0.2 0.1 0.0 -0.1 -0.2 2 1 0 -1 -2 Normal Score Residual Normal Probability Plot of the Residuals (response is Output)
3 14.1 14.0 13.9 13.8 0.2 0.1 0.0 -0.1 -0.2 Fitted Value Residual Residuals Versus the Fitted Values (response is Output) 5 4 3 2 1 0.2 0.1 0.0 -0.1 -0.2 Loom Residual Residuals Versus Loom (response is Output)

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4 13.4. An article in the Journal of the Electrochemical Society (Vol. 139, No. 2, 1992, pp.
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Assignment_Solution_Chp._13 - Chapter 13 Solutions 13.1 A...

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