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 770 1,790 2,230

1,490 1,660 1,620

820 1,640 1,720

Slant 1,420 1,830 2,070

1,710 1,780 1,510

1,240 1,670 2,490

Rear-end. 740 810 1,640

1,290 1,550 1,620

960 1,200 1,210

Click here for the Excel Data File

(a-1)Choose the correct row-effect hypotheses.

a.H₀:A₁A₂A₃ 0

Angle means differH₁: All theA_jare equal to zero

Angle means are the sameb.H₀:A₁=A₂=A₃= 0

Angle means are the sameH₁: Not all theA_jare equal to zero

Angle means differ

multiple choice 1

• b
• a

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

a.H₀:B₁B₂B₃ 0

Vehicle means differH₁: All theB_kare equal to zero

Vehicle means are the sameb.H₀:B₁=B₂=B₃= 0

Vehicle means are the sameH₁: Not all theB_kare equal to zero

Vehicle means differ

multiple choice 2

• a
• b

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

a.H₀: Not all theAB_jkare equal to zero

there is an interaction effectH₁: All theAB_jkare equal to zero

there is no interaction effectb.H₀: All theAB_jkare equal to zero

there is no interaction effectH₁: Not all theAB_jkare equal to zero

there is an interaction effect

multiple choice 3

• a
• b

(b)Fill in the missing data.(Round your table of means valuesto 1 decimal place,SSandFvalues to 2 decimal places,MSvalues to 3 decimal places, andp-values to 4 decimal places.)

Table of MeansFactor 2 (Vehicle)

Factor 1 (Angle). Goliath Varmint Weasel Total

Head-On

Slant

Rear-End

Total

Two-Factor ANOVA with Replication SS df MS F p-value

Factor 1 (Angle)

Factor 2 (Vehicle)

Interaction

Error

Total

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

multiple choice 4

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