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

4:	319.2	409.5	311.0	326.5	316.8	349.8	309.7
6:	441.1	347.2	361.0	404.5	331.0	348.9	381.7
8:	390.4	366.2	351.0	357.1	409.9	367.3	382.0
10:	364.7	452.9	461.4	433.1	410.6	384.2	362.6
12:	408.4	441.8	419.9	410.7	473.4	441.2	465.8

Does variation in plate length have any effect on true averageaxial stiffness? State the relevant hypotheses using analysis ofvariance.

H₀: μ₁ ≠μ₂ ≠ μ₃ ≠μ₄ ≠ μ₅
H_a: at least twoμ_i's are equalH₀:μ₁ ≠ μ₂ ≠μ₃ ≠ μ₄ ≠μ₅
H_a: all five μ_i'sare equal    H₀:μ₁ = μ₂ =μ₃ = μ₄ =μ₅
H_a: all five μ_i'sare unequalH₀: μ₁ =μ₂ = μ₃ =μ₄ = μ₅
H_a: at least twoμ_i's are unequal

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

Source	Degreesof freedom	Sum of Squares	Mean Squares	f
Treatments
Error
Total

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

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

P-value > 0.1000.050 < P-value <0.100    0.010 < P-value <0.0500.001 < P-value < 0.010P-value <0.001

State the conclusion in the problem context.

Fail to reject H₀. There are no differencesin the true average axial stiffness for the different platelengths.Reject H₀. There are differences in thetrue average axial stiffness for the different platelengths.    Reject H₀.There are no differences in the true average axial stiffness forthe different plate lengths.Fail to reject H₀.There are differences in the true average axial stiffness for thedifferent plate lengths.