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.
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.
(d) Perform Tukey multiple comparison tests. (Input the
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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