The cathode warm-up time (in seconds) was determined for three different types of X-ray tubes using fifteen observations of each type. The results are listed in the following table.

Do an analysis of variance on these data and test the hypothesis that the three tube types require the same average warm-up time. Include a pair of orthogonal contrasts in your ANOVA table. Define one of the contrasts so it tests H0: μA = μC. What does the other contrast test? Check to see that the sums of squares associated with your two contrasts verify the statement of Theorem 12.4.1.

Warm-Up Times (sec) Tube Type 19 27 20 2416 14 23 31 20 2526 18 26 25 32 2915 19 18 22 27 318 21 20 23 40 24 1917 20 27 24 25 17 19 18 29 22 32 19 18 35 18 18