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 ($) Goliath Crash Type Head-On Slant Rear-end 730 1,420 810 1,400 1,750 1,260 710 1,290 910 a Varmint 1,710 1,610° 1,610 1,860 1,780 1,670 860 1,560 1,240 Weasel 2,230 1,600 1,730 2,040 1,510 2,470 1,660 1,620 1,260 Click here for the Excel Data File (8-1) Choose the correct row-effect hypotheses. a. Ho: A₁ A2 A3 #0 Angle means differ H₁: All the Ajare equal to zero Angle means are the same b. Ho: A1 A2 A3=0 Angle means are the same H₁: Not all the Ajare equal to zero Angle means differ (a-2) Choose the correct column-effect hypotheses. Vehicle means differ Bk are equal to zero Vehicle means are the same means are the same a. Ho B₁ B2 B3 #0 H: All the b. Ho: B₁ B2= B3=0 Vehicle H: Not all the Bk are equal to zero Vehicle means differ

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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 (S)
Crash Type
Goliath
Head-On
Slant
Rear-end
b
730
1,420
810
a
1,400
1,750
1,260
710
1,290
,910
Varmint
1,710
1,610
1,610
1,860
1,780
1,670
860
1,560
1,240
Weasel
2,230
1,600
1,730
2,040
1,510
2,470
1,660
Click here for the Excel Data File
(a-1) Choose the correct row-effect hypotheses.
a. Ho: A1 A2 A3 #0
Angle means differ
H: All the Ajare equal to zero Angle means are the same
b. Ho: A1 A2 A3=0
Angle means are the same.
H: Not all the Ajare equal to zero
Angle means differ
1,620
1,260
(8-2) Choose the correct column-effect hypotheses.
a. Ho B1 B2 B3 #0
Vehicle means differ
H: All the Bk are equal to zero Vehicle means are the same
Vehicle means are the same
b. Ho: B₁ B2 B3=0
H: Not all the Bk are equal to zero Vehicle means differ
Transcribed Image Text: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 (S) Crash Type Goliath Head-On Slant Rear-end b 730 1,420 810 a 1,400 1,750 1,260 710 1,290 ,910 Varmint 1,710 1,610 1,610 1,860 1,780 1,670 860 1,560 1,240 Weasel 2,230 1,600 1,730 2,040 1,510 2,470 1,660 Click here for the Excel Data File (a-1) Choose the correct row-effect hypotheses. a. Ho: A1 A2 A3 #0 Angle means differ H: All the Ajare equal to zero Angle means are the same b. Ho: A1 A2 A3=0 Angle means are the same. H: Not all the Ajare equal to zero Angle means differ 1,620 1,260 (8-2) Choose the correct column-effect hypotheses. a. Ho B1 B2 B3 #0 Vehicle means differ H: All the Bk are equal to zero Vehicle means are the same Vehicle means are the same b. Ho: B₁ B2 B3=0 H: Not all the Bk are equal to zero Vehicle means differ
(a-3) Choose the correct interaction-effect hypotheses.
a. Ho: Not all the ABjk are equal to zero there is an Interaction effect
H₁: All the ABjk are equal to zero
b. Ho: All the ABjk are equal to zero
H: Not all the ABjk are equal to zero
a
(b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and Fvalues to 2 decimal places, MS values to
3 decimal places, and p-values to 4 decimal places.)
Factor 1 (Angle)
Head-On
Slant
Rear-End
Total
Source
Factor 1 (Angle)
Factor 2 (Vehicle)
Interaction
Error
Total
there is no Interaction effect
there is no Interaction effect
there is an interaction effect
Table of Means
Goliath
SS
Factor 2 (Vehicle)
Varmint
Weasel
Two-Factor ANOVA with Replication
df
Total
MS
F
p-value
Transcribed Image Text:(a-3) Choose the correct interaction-effect hypotheses. a. Ho: Not all the ABjk are equal to zero there is an Interaction effect H₁: All the ABjk are equal to zero b. Ho: All the ABjk are equal to zero H: Not all the ABjk are equal to zero a (b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and Fvalues to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.) Factor 1 (Angle) Head-On Slant Rear-End Total Source Factor 1 (Angle) Factor 2 (Vehicle) Interaction Error Total there is no Interaction effect there is no Interaction effect there is an interaction effect Table of Means Goliath SS Factor 2 (Vehicle) Varmint Weasel Two-Factor ANOVA with Replication df Total MS F p-value
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