A clay tile company is interested in studying the effect of cooling temperature

on strength. The company has five ovens which produce the tiles. Four tiles were baked

in each oven and then randomly assigned to one of the four cooling temperatures. The

data are shown below.

(a) Which type of design was employed? Describe how the fundamental

principles of experimental design were followed in this design.

(b) If SSE = 75:3, compute the F-statistic by hand (without using any

code) to determine if there is a difference among the four cooling temperatures

(use alpha= 0.01). Show your work.

(c) Estimate the relative efficiency and interpret your result.

(d) If there is a difference among the four temperatures, perform pairwise

comparisons using Tukey's procedure. Calculate by hand rst, then use SAS to

verify your calculations.

(e) Suppose the company believes there is a jump in the strength at 12.5,

but otherwise cooling temperature has no effect, that is, 5 and 10 are not different,

neither are 15 and 20, but these two groups of temperatures have different effects.

Find a set of orthogonal contrasts that would allow you to test this.

(f) Test these contrasts using SAS (or by hand). State your conclusions.

(g) An expert suspects that it may not be proper to assume an additive

model. Use Tukey's test for non-additivity to settle this issue. Write conclusion clearly.

\f