HW4_sol_121010

# HW4_sol_121010 - ISyE 2028C Solution for HW#4 Problem#2 The...

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ISyE 2028C Solution for HW#4 Problem #2: The following table reports the investigation of the impact of different amount of dye used on fabric color density. Two plants are randomly selected among 10 plants owned by the company for this investigation. There are four replicates in each testing case. Amount of Dye Plant 0.33% 1% 3% 1 5.2, 6.0, 5.9, 5.9 12.3, 10.5, 12.4, 10.9 22.4, 17.8, 22.5, 18.4 2 6.5, 5.5, 6.4, 5.9 14.5, 11.8, 16.0, 13.6 29.0, 23.2, 29.7, 24.0 Answer the following questions. (a) What is the model for the data presented in the table? (b) What are the definitions of the sums of squares in terms of data notation? Note that there are several sums of squares. (c) What assumption(s) are needed to conduct an ANOVA test of whether the population means from three different amounts of dye are the same? Here, the mean is the average of color densities. (d) What are the degrees of freedom for the sums of squares? (e) What is the formula of the F-test in the end of the ANOVA table? What are the degrees of freedoms for the F-distribution? If α = 0.01, what is the F-table value?

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HW4_sol_121010 - ISyE 2028C Solution for HW#4 Problem#2 The...

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