12.60 To compare the preferences of technicians for three brands of calculators, each of three technicians was required to perform an identical series of calculations on each of the three calculators, A, B, and C. To avoid the possibility of fatigue, a suitable time period separated each set of calculations, and the calculators were used in random order by each technician. A preference rating, based on a 0–100 scale, was recorded for each machine/technician combination. These data are shown in table below.

a Do the data provide sufficient evidence to indicate a difference in technician preference among the three brands? Use .
b Why did the experimenter have each technician test all three calculators? Why not randomly assign three different technicians to each calculator?

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Calculator Brand Technician A B -23 1 85 90 95 70 70 75 65 60 80