Question: Students Bauer, Brinnk, and Fife studied the performance of 3 different copy machines. m = 5 copies of the same CAD drawing were made on each machine for 3 different enlargement settings, and the length of a particular line segment on that drawing was measured. (All the measuring was done by a single student, and as a means of getting a handle on measurement precision, that student measured the line on the original drawing 10 times, obtaining lengths with sample mean 2.0058 in and sample standard deviation .0008 in.) Sample means and standard deviations for the measurements on the copies are below.

(a) Is it a surprise that = .0017 is larger than the .0008 in standard deviation obtained in the preliminary measurement study? Why or why not?

(b) The m = 5 measurements from copier 1 at the 100 % setting were in fact 2.014, 2.020, 2.017, 2.015, and 2.013. What are the values of the corresponding residuals?

(c) Is it possible from what is given to find all the residuals? How might one use all the residuals?

(d) Four of the 9 fitted copier × enlargement setting interactions are ab11 = -.00296, ab12 = -.00142, ab21 = .00264, and ab22 = .00038. Find the other five interactions.

(e) Are ANY of the nine interactions statistically detectable (using, say 95 % two-sided confidence limits for each interaction as a basis of judging this)?

(f) Give 95 % individual two-sided confidence limits for the difference in copier 1 and 2 main effects, α1-α2. Is it credible to use your interval for every level of enlargement? Why or why not? (Hint: consider your answer to part (e).)

(g) Make an interaction plot for the set of means. Let the horizontal axis correspond to enlargement setting and the vertical axis correspond to mean line length. You should have one trace for each level of copier. How does your plot support your answer to (e)?