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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 32PPS

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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.

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
357.1 409.9 367.3 382.0
8: 393.4 366.2 351.0
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
USE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
O Ho: M₁ M₂ M3 M4 M5
#
#
H₂: at least two μ's are equal
O Ho: M₁ = M₂ = μ3 = μ¹4 = μ5
H₂: all five μ's are unequal
Ho: M₁ = μ₂ = μ3 = μ 4 = μ5
H₂: at least two μ's are unequal
a
Ho: M₁ M₂ ‡μ3 ‡ M4 ‡ M5
H₂: all five μ's are equal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Degrees of
freedom
Sum of
Squares
Mean
Squares
Source
Error
Total
Treatments
Give the test statistic. (Round your answer to two decimal places.)
f =
f

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