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: 302.2 409.5 311.0 326.5 316.8 349.8 309.7

6: 412.1 347.2 361.0 404.5 331.0 348.9 381.7

8: 386.4 366.2 351.0 357.1 409.9 367.3 382.0

10: 364.7 452.9 461.4 433.1 410.6 384.2 362.6

12: 416.4 441.8 419.9 410.7 473.4 441.2 465.8

1. Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. Select an answer.

A)H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 Ha: all five μi's are equal

B)H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 Ha: at least two μi's are equal

C)H0: μ1 = μ2 = μ3 = μ4 = μ5 Ha: all five μi's are unequal

D)H0: μ1 = μ2 = μ3 = μ4 = μ5 Ha: at least two μi's are unequal

2.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: __________ | ____________ | ___________ | _______ |

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

f = ?

4. What can be said about the P-value for the test? Select an answer

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

5.State the conclusion in the problem context. Select an answer

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

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

Answer 1

1)

D)H0: μ1 = μ2 = μ3 = μ4 = μ5 Ha: at least two μi's are unequal

2)

Source of Variation	df	SS	MS	F
Between Groups	4	46348.01	11587.00	11.56
Within Groups	30	30071.00	1002.37
Total	34	76419.01

3) test statistic f =11.56

4) E)P-value < 0.001

5)

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