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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 | |
(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 |
(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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