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: 323.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 423.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 393.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 418.4 441.8 419.9 410.7 473.4 441.2 465.8 Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5 Ha: at least two ?i's are equalH0: ?1 = ?2 = ?3 = ?4 = ?5 Ha: all five ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5 Ha: at least two ?i's are unequalH0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5 Ha: all five ?i's are equal Test the relevant hypotheses using analysis of variance with ? = 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 > 0.1000.050 < 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. Reject H0. There are no 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. Fail to reject H0. There are differences in the true average axial stiffness for the different plate lengths.Fail to reject H0. There are no differences in the true average axial stiffness for the different plate lengths.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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:	323.2	409.5	311.0	326.5	316.8	349.8	309.7
6:	423.1	347.2	361.0	404.5	331.0	348.9	381.7
8:	393.4	366.2	351.0	357.1	409.9	367.3	382.0
10:	362.7	452.9	461.4	433.1	410.6	384.2	362.6
12:	418.4	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: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄ ≠ ?₅
H_a: at least two ?_i's are equalH₀: ?₁ = ?₂ = ?₃ = ?₄ = ?₅
H_a: all five ?_i's are unequal H₀: ?₁ = ?₂ = ?₃ = ?₄ = ?₅
H_a: at least two ?_i's are unequalH₀: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄ ≠ ?₅
H_a: all five ?_i's are equal

Test the relevant hypotheses using analysis of variance with ? = 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 > 0.1000.050 < 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.

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