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Homework09Solns

# Homework09Solns - Stat 512 2 Solutions to Homework#9 Dr...

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Stat 512 – 2 Solutions to Homework #9 Dr. Simonsen Due November 2, 2005 by 4:30pm 1. KNNL 19.4: In a two-factor study, the treatment means μ ij are as follows: Factor B Factor A B B 1 B B 2 B B 3 A 1 34 23 36 A 2 40 29 42 a. Obtain the factor A level means. 1 2 34 23 36 40 29 42 ˆ ˆ 31, 37 3 3 + + + + μ = = μ = = i i b. Obtain the main effects of factor A. 1 1 2 2 34 23 36 40 29 42 ˆ 34 6 ˆ ˆ ˆ 31 34 3 ˆ ˆ ˆ 37 34 3 + + + + + μ = = α = μ −μ = = − α = μ −μ = = + i i c. Does the fact that μ 12 μ 11 = –11 while μ 13 μ 12 = 13 imply that factors A and B interact? Explain. No. An interaction effect cannot be established by considering only a single level of factor A. This difference is completely attributable to the main effect of factor B. d. Prepare a treatment means plot and determine whether the two factors interact. What do you find? The lines are completely parallel. The treatment means plot indicates no interaction.

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2. Recall the Filling Machines data set used in Homework #7-8. In that data set, there were three columns (Y , machine, and carton). Is carton (with levels 1-20) a second treatment factor that one could have included in the model? Explain. (HINT: How many cartons are really used in this experiment, 20 or 120? Would that column be a meaningful variable to include in your analysis?). No. There are actually 120 cartons used in this experiment. The “carton” label is not actually a factor. It is simply a label to identify which of the 20 randomly selected cartons for a particular machine is referred to. However, carton 6 (say) from machine 1 has no relationship to carton 6 from machine 2. For the remaining questions use the Hay Fever Relief dataset from problem 19.14 described on page 868 of KNNL. 3. Give a table of sample sizes, means, and standard deviations for the nine different treatment combinations. Level of Level of ------------relief----------- A B N Mean Std Dev 1 1 4 2.4750000 0.17078251 1 2 4 4.6000000 0.29439203 1 3 4 4.5750000 0.17078251 2 1 4 5.4500000 0.26457513 2 2 4 8.9250000 0.17078251 2 3 4 9.1250000 0.30956959 3 1 4 5.9750000 0.22173558 3 2 4 10.2750000 0.33040379 3 3 4 13.2500000 0.20816660 4. Write the factor effects model for this analysis, and estimate the parameters of this model under the zero-sum constraint system (i.e. the one described on page 816 of the text). Also demonstrate that your estimates do in fact satisfy these constraints.
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