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

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.