Reconsider the axial stiffness data given in Exercise 8.

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 5 32.39 MSE 5 13.929 x3. 5 427.5 x2. 5 502.8 x3. 5 427.5 a 5 .05 MSE 5 272.8 x5# 5 532.1 x1# 5 462.0, x2# 5 512.8, x3# 5 437.5, x4# 5 469.3

(ft2

/gal)

(J 5 4)

Tukey’s pairwise comparisons Family error rate Individual error rate Critical value Intervals for (column level mean) – (row level mean)

4 6 810 6

15.4 8

8.3 43.1 10 10.9 18.0 12 20.4

a. Is it plausible that the variances of the five 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.