16. Reconsider the axial stiffness data given in Exercise 7. ANOVA output from MINITAB follows:

Analysis of Variance for stiffness Source DF SS MS F P length 4 43993 10998 10.48 0.000 Error 30 31475 1049 Total 34 75468 Level N Mean StDev 4 7 333.21 36.59 6 7 368.06 28.57 8 7 375.13 20.83 10 7 407.36 44.51 12 7 437.17 26.00 Pooled StDev  32.39 Tukey’s pairwise comparisons Family error rate  0.0500 Individual error rate  0.00693 Critical value  4.10 Intervals for (column level mean)  (row level mean)

4 6 8 10 6 85.0 15.4 8 92.1 57.3 8.3 43.1 10 124.3 89.5 82.4

23.9 10.9 18.0 12 154.2 119.3 112.2 80.0

53.8 18.9 11.8 20.4

a. Is it plausible that the variances of the ve axial stiffness index distributions are identical?

Explain.

b. Use the output (without reference to our F table)

to test the relevant hypotheses.

c. Use the Tukey intervals given in the output to determine which means differ, and construct the corresponding underscoring pattern.