Using \(q_{0.01}=5.499\) for the Tukey HSD method, examine differences among the ball bearings in Exercise 12.19.

Data From Exercise 12.19

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12.19 Concerns about the increasing friction between some machine parts prompted an investigation of four dif- ferent types of ball bearings. Five different machines were available and each type of ball bearing was tried in each machine. Given the observations on tempera- ture, coded by subtracting the smallest value, Machines 1 2 34 5 Ball bearing 110 8 7 4 6 Ball bearing 2 10 7 12 5 11 Ball bearing 3 8 9 11 12 10 Ball bearing 4 12 8 6 11 13 (a) decompose each observation yij as - yijy..+(yi.y..) + (.jy..) +(Vij-Yi-yj+y..) (b) obtain the sum of squares and the degrees of free- dom for each component; (c) construct the analysis of variance table and test for differences among the bearings using = 0.01.