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: Not all the Aj are equal to zero ⇐⇐ Angle means differ   a b   (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 same b. 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 effect b. 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) 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 α = 0.05, choose the correct statements.   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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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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 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. H0A1 ≠ A2 ≠ A3 ≠ 0 ⇐⇐ Angle means differ
  H1: All the Aj are equal to zero ⇐⇐ Angle means are the same
b. H0A1 = A2 = A3 = 0 ⇐⇐ Angle means are the same
  H1: Not all the Aj are equal to zero ⇐⇐ Angle means differ

 

  • a
  • b


 
(a-2) C
hoose the correct column-effect hypotheses.
 

 

a. H0B1 ≠ B2 ≠ B3 ≠ 0 ⇐⇐ Vehicle means differ
  H1: All the Bk are equal to zero ⇐⇐ Vehicle means are the same
b. H0B1 = 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 effect
b. 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) 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 α = 0.05, choose the correct statements.
 

  • 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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