Question

A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:

4: 342.2 409.5 311.0 326.5 316.8 349.8 309.7

6: 420.1 347.2 361.0 404.5 331.0 348.9 381.7

8: 398.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 366.7 452.9 461.4 433.1 410.6 384.2 362.6

12: 417.4 441.8 419.9 410.7 473.4 441.2 465.8

Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. H0: μ1 = μ2 = μ3 = μ4 = μ5 Ha: all five μi's are unequal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 Ha: at least two μi's are equal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 Ha: all five μi's are equal H0: μ1 = μ2 = μ3 = μ4 = μ5 Ha: at least two μi's are unequal

Test the relevant hypotheses using analysis of variance with α = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)

Source Degrees of freedom Sum of Squares Mean Squares f

Treatments

Error

Total

Give the test statistic. (Round your answer to two decimal places.) f =

What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001

State the conclusion in the problem context. Fail to reject H0. There are no differences in the true average axial stiffness for the different plate lengths. Reject H0. There are no differences in the true average axial stiffness for the different plate lengths. Fail to reject H0. There are differences in the true average axial stiffness for the different plate lengths. Reject H0. There are differences in the true average axial stiffness for the different plate lengths. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: Option D is correct.

ANOVA table:

Source	DF	SS	MS	F-Stat
Columns	4	41987.87	10496.97	10.51
Error	30	29971.75	999.06
Total	34	71959.61

Test statistic = 10.51

P-value < 0.001

Conclusion: Option D is correct.