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.
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
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
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.
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