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# Problem 1:In a study of four electroplating processes, an engineer obtained twelve

homogeneous wire rods, each ¼ inch in diameter, from each of five different suppliers (60 rods total). The rods were assigned to the electroplating processes as in a GRCBD: those from each supplier were divided evenly and assigned to the four different electroplating processes. After all 60 rods were electroplated, the average thickness (in units of 100mm) of each rod was measured, producing the data in the table below. (Each cell of the table lists a single thickness measurement.) The data is linked below.

Process Supplier

1 2 3 4 5

A 18.6 19.7 19.2 18.3 19.1

19.2 19.2 19.4 18 19.6

19 18.9 19.4 18.4 19.7

B 21.4 21.8 19.9 22.4 20.6

22 21.8 20.1 22.1 21.2

21.3 21.7 19.6 22.3 21.3

C 17.4 18.3 18.7 20.1 19.4

17.6 18.3 18.7 20.2 19.3

17.9 18.3 18.9 20.4 19.6

D 19.3 20.6 20 19.6 20.3

19.7 20.1 20.4 19.5 20.3

19.8 19.7 20.5 19.9 20.8

Question 1:

Create the Block-Treatment Interaction Plot. Based on visual assessment, which of the statements bests describes the interaction pattern?

a. The treatment effects follow very different patterns for each supplier suggesting strong indications of anti-directional interaction.

b. The treatment effects appear to follow approximately the same pattern for each supplier, but there are also weak indications of nonadditivity (interactions).

c. The treatment effects follow exactly the same pattern for all suppliers, so there is no indication of a significant interaction.

Question 2:

Create the Treatment Effect Plot (Main Effect plot). This is a plot of the treatment means versus the treatment. Compare this plot with that of Question 1. Does the pattern exhibited here provide a meaningful description of the overall pattern of treatment effects?

a. No, the main effect plot has a very different pattern from the pattern exhibited in the graph in Question 1.

b. Yes, the main effect plot does appear to capture the general pattern of the treatment effects exhibited in the graph of Question 1.

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