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:	308.2	409.5	311.0	326.5	316.8	349.8	309.7
6:	431.1	347.2	361.0	404.5	331.0	348.9	381.7
8:	388.4	366.2	351.0	357.1	409.9	367.3	382.0
10:	355.7	452.9	461.4	433.1	410.6	384.2	362.6
12:	415.4	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.

a) H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
b) H_a: at least two μ_i's are unequalH₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
c) H_a: all five μ_i's are equal    H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
d) H_a: at least two μ_i's are equalH₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
e) H_a: all five μ_i'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

(the last column its just f)

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

What can be said about the P-value for the test?

a) P-value > 0.100

b) 0.050 < P-value < 0.100    

c) 0.010 < P-value < 0.050

d) 0.001 < P-value < 0.010

e) P-value < 0.001

State the conclusion in the problem context.

a) Reject H₀. There are no differences in the true average axial stiffness for the different plate lengths.

b) Fail to reject H₀. There are differences in the true average axial stiffness for the different plate lengths.   

c) Reject H₀. There are differences in the true average axial stiffness for the different plate lengths.

d) Fail to reject H₀. There are no differences in the true average axial stiffness for the different plate lengths.

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: Option A is correct.

ANOVA table:

Source	Degrees of freedom	Sum of Squares	Mean Squares	f
Treatments	4	44591.61	11147.90	10.24
Error	30	32650.92	1088.36
Total	34	77242.53

Test statistic = 10.24

P-value < 0.001

Conclusion: Option C is correct.