Chapter 9.4, Problem 4E

Three different corrosion-resistant coatings are being considered for use on iron pipes. Ten pieces of pipe are marked off in six equal segments. For each pipe, two segments received coating A, two received coating B, and the remaining two received coating C. The pipes were placed in a corrosive environment for a period of time: then the depth of the deepest pit (in mm) caused by corrosion was measured for each segment on each pipe. The effect of interest is the coating; the pipe is a blocking factor, and there were two replications on each pipe. The following sums of squares were calculated: sum of squares for blocks = 11.2, sum of squares for treatments = 4.8, sum of squares for interactions = 18.4, total sum of squares = 44.7.

1. a. Construct an ANOVA table. You may give ranges for the P-values.
2. b. Are the assumptions for a randomized complete block design satisfied? Explain.
3. c. Does the ANOVA table provide evidence that mean pit depth differs among coatings? Explain.