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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 TypeGoliathVarmintWeaselHead-On7201,7002,290 1,4201,6601,680 8701,6401,700Slant1,4401,8102,060 1,7201,7501,510 1,2601,6202,480Rear-end7308201,650 1,2701,5401,670 9301,2201,280
 


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

-b
-a

 
(a-2) Choose the correct column-effect hypotheses.
 a.H0: B1 ≠ B2 ≠ B3 ≠ 0⇐
⇐ Vehicle means differ H1: All the Bk are equal to zero⇐
⇐ Vehicle means are the sameb.H0: B1 = B2 = B3 = 0⇐
⇐ Vehicle means are the same H1: Not all the Bk are equal to zero⇐
⇐ Vehicle means differ
 

-a
-b

 
(a-3) Choose the correct interaction-effect hypotheses.
 a.H0: Not all the ABjk are equal to zero⇐
⇐ there is an interaction effect H1: All the ABjk are equal to zero⇐
⇐ there is no interaction effectb.H0: All the ABjk are equal to zero⇐
⇐ there is no interaction effect H1: Not all the ABjk are equal to zero⇐
⇐ there is an interaction effect
 

-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)GoliathVarmintWeaselTotalHead-OnSlantRear-EndTotal
 
Two-Factor ANOVA with ReplicationSourceSSdfMSFp-valueFactor 1 (Angle)Factor 2 (Vehicle)InteractionError  Total   
 
(c) Using α = 0.05, choose the correct statement.
 

-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 3 decimal places.)
 
Post hoc analysis for Factor 1:
 Tukey simultaneous comparison t-values (d.f. = 18)  Rear-EndHead-OnSlant  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)
  GoliathVarmintWeasel  Goliath   Varmint  Weasel critical values for experimentwise error rate:  0.05   0.01 
rev: 05_03_2019_QC_CS-167888

Step-by-step answer

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