Problem 13.15 The data in the next table are the results of an experiment to investigate the sources of variability in testing the strength of Portland cement. A sample of cement was divided into small samples for testing. The cement was “gauged” (mixed with water) by three different men called gaugers, and then it was cast into cubes. Three men, called breakers, later tested the cubes for compressive strength. The measurements are in pounds per square inch. Each gauger gauged 12 cubes, which were then divided into three sets of four, and each breaker tested one set of four cubes from each gauger. All the tests were carried out on the same machine. The purpose of the experiment was to identify the source of and measure the variability among gaugers and breakers.

(a) Compute the estimated cell means and display your results in the format of Table 13.9.

(b) Plot the estimated cell means of the breakers (factor B) against the the three levels of gaugers (factor A) (see Figure 13.6 for an example). Does the graph suggest the existence of an interaction?

(c) Test for the existence of main effects and interactions by constructing the ANOVA table.

(d) Check the model assumptions by graphing suitable residual plots. Breaker (B) Gauger (A) Breaker 1 Breaker 2 Breaker 3 Gauger 1 5280 5520 4340 4400 4160 5180 4760 5800 5020 6200 5320 4600 Gauger 2 4420 5280 5340 4880 4180 4800 5580 4900 4960 6200 4600 4480 Gauger 3 5360 6160 5720 4760 4460 4930 5680 5500 5620 5560 4680 5600