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 H 0 A 1 A 2 A 3 0 Angle means differ H 1 All the A j are equal to zero Angle means are the same b H 0 A 1 A 2 A 3 0 Angle means are the same H 1 Not all the A j are equal to zero Angle means differ multiple choice 1 a b (a 2) C hoose the correct column effect hypotheses a H 0 B 1 B 2 B 3 0 Vehicle means differ H 1 All the B k are equal to zero Vehicle means are the same b H 0 B 1 B 2 B 3 0 Vehicle means are the same H 1 Not all the B k are equal to zero Vehicle means differ multiple choice 2 a b (a 3) Choose the correct interaction effect hypotheses a H 0 Not all the AB jk are equal to zero there is an interaction effect H 1 All the AB jk are equal to zero there is no interaction effect b H 0 All the AB jk are equal to zero there is no interaction effect H 1 Not all the AB jk are equal to zero there is an interaction effect multiple choice 3 a b (b) Fill in the missing data (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p values to 4 decimal places ) Table of Means Factor 2 (Vehicle) Factor 1 (Angle) Goliath Varmint Weasel Total Head On Slant Rear End Total Two Factor ANOVA with Replication Source SS df MS F p value Factor 1 (Angle) Factor 2 (Vehicle) Interaction Error Total (c) Using 0 05, choose the correct statements multiple choice 4 The main effects of angle and vehicle are significant, but there is not a significant interaction effect The main effect of vehicle is significant however, there is no significant effect from angle or interaction between angle and vehicle The main effect of angle is significant however, there is no significant effect from vehicle or interaction between angle and vehicle (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 1 decimal place ) Post hoc analysis for Factor 1 Tukey simultaneous comparison t values ( d f 18) Rear End Head On Slant Rear End Head On Slant Critical values for experimentwise error rate 0 05 0 01 Post hoc analysis for Factor 2 Tukey simultaneous comparison t values ( d f 18) Goliath Varmint Weasel Goliath Varmint Weasel critical values for experimentwise error rate 0 05 0 01

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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

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 A_j are equal to zero	Angle means are the same
b.	H₀: A₁ = A₂ = A₃ = 0	Angle means are the same
	H₁: Not all the A_j are equal to zero	Angle means differ

multiple choice 1

(a-2) Choose the correct column-effect hypotheses.

a.	H₀: B₁ B₂ B₃ 0	Vehicle means differ
	H₁: All the B_k are equal to zero	Vehicle means are the same
b.	H₀: B₁ = B₂ = B₃ = 0	Vehicle means are the same
	H₁: Not all the B_k are equal to zero	Vehicle means differ

multiple choice 2

(a-3) Choose the correct interaction-effect hypotheses.

a.	H₀: Not all the AB_jk are equal to zero	there is an interaction effect
	H₁: All the AB_jk are equal to zero	there is no interaction effect
b.	H₀: All the AB_jk are equal to zero	there is no interaction effect
	H₁: Not all the AB_jk are equal to zero	there is an interaction effect

multiple choice 3

(b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.)

Table of Means
	Factor 2 (Vehicle)
Factor 1 (Angle)	Goliath	Varmint	Weasel	Total
Head-On
Slant
Rear-End
Total

Two-Factor ANOVA with Replication
Source	SS	df	MS	F	p-value
Factor 1 (Angle)
Factor 2 (Vehicle)
Interaction
Error
Total

(c) Using = 0.05, choose the correct statements.

multiple choice 4

The main effects of angle and vehicle are significant, but there is not a significant interaction effect.
The main effect of vehicle is significant; however, there is no significant effect from angle or interaction between angle and vehicle.
The main effect of angle is significant; however, there is no significant effect from vehicle or interaction between angle and vehicle.

(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 1 decimal place.) Post hoc analysis for Factor 1: