Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 9.2, Problem 2E
The article “Optimum Design of an A-pillar Trim with Rib Structures for Occupant Head Protection” (H. Kim and S. Kang. Proceedings of the Institution of Mechanical Engineers. 2001:1161–1169) discusses a study in which several types of A-pillars were compared to determine which provided the greatest protection to occupants of automobiles during a collision. Following is a one-way ANOVA table, where the treatments are three levels of longitudinal spacing of the rib (the article also discussed two insignificant factors, which are omitted here). There were nine replicates at each level. The response is the head injury criterion (HIC), which is a unitless quantity that measures the impact energy absorption of the pillar.
The treatment means were
- a. Can you conclude that the longitudinal spacing affects the absorption of impact energy?
- b. Use the Tukey–Kramer method to determine which pairs of treatment means, if any. are different at the 5% level.
- c. Use the Bonferroni method to determine which pairs of treatment means, if any, are different at the 5% level.
- d. Which method is more powerful in this case, the Tukey-Kramer method or the Bonferroni method?
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In a bumper test, three test vehicles of each of three types of autos were crashed into a barrier at 5 mph, and the resulting damage was estimated. Crashes were from three angles: head-on, slanted, and rear-end. The results are shown below. Research questions: Is the mean repair cost affected by crash type and/or vehicle type? Are the observed effects (if any) large enough to be of practical importance (as opposed to statistical significance)?
5 mph Collision Damage ($)
Crash Type
Goliath
Varmint
Weasel
Head-On
750
1,740
2,250
1,400
1,660
1,690
800
1,630
1,740
Slant
1,450
1,800
2,080
1,790
1,750
1,500
1,270
1,600
2,410
Rear-end
720
870
1,660
1,240
1,580
1,670
940
1,290
1,210
Click here for the Excel Data File
(a-1) Choose the correct row-effect hypotheses.
a.
H0: A1 ≠ A2 ≠ A3 ≠ 0
⇐⇐ Angle means differ
H1: All the Aj are equal to zero
⇐⇐ Angle means are the same
b.
H0: A1 = A2 = A3 = 0
⇐⇐ Angle means are the same
H1:…
In a bumper test, three test vehicles of each of three types of autos were crashed into a barrier at 5 mph, and the resulting damage was estimated. Crashes were from three angles: head-on, slanted, and rear-end. The results are shown below. Research questions: Is the mean repair cost affected by crash type and/or vehicle type? Are the observed effects (if any) large enough to be of practical importance (as opposed to statistical significance)?
5 mph Collision Damage ($)
Crash Type
Goliath
Varmint
Weasel
Head-On
700
1,700
2,280
1,400
1,650
1,670
850
1,630
1,740
Slant
1,430
1,850
2,000
1,740
1,700
1,510
1,240
1,650
2,480
Rear-end
700
860
1,650
1,250
1,550
1,650
970
1,250
1,240
(d) Perform Tukey multiple comparison tests. (Input the mean values within the input boxes of the first row and input boxes of the first column. Round your t-values and critical values to 2 decimal places and other answers to 3 decimal places.) Post hoc analysis…
In a bumper test, three test vehicles of each of three types of autos were crashed into a barrier at 5 mph, and the resulting damage was estimated. Crashes were from three angles: head-on, slanted, and rear-end. The results are shown below. Research questions: Is the mean repair cost affected by crash type and/or vehicle type? Are the observed effects (if any) large enough to be of practical importance (as opposed to statistical significance)?
5 mph Collision Damage ($)
Crash Type
Goliath
Varmint
Weasel
Head-On
700
1,700
2,280
1,400
1,650
1,670
850
1,630
1,740
Slant
1,430
1,850
2,000
1,740
1,700
1,510
1,240
1,650
2,480
Rear-end
700
860
1,650
1,250
1,550
1,650
970
1,250
1,240
Click here for the Excel Data File
(a-1) Choose the correct row-effect hypotheses.
a.
H0: A1 ≠ A2 ≠ A3 ≠ 0
⇐⇐ Angle means differ
H1: All the Aj are equal to zero
⇐⇐ Angle means are the same
b.
H0: A1 = A2 = A3 = 0
⇐⇐ Angle means are the same
H1:…
Chapter 9 Solutions
Statistics for Engineers and Scientists
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