Choose the conclusions below that are appropriate for these data. (Select all th
ID: 3044950 • Letter: C
Question
Choose the conclusions below that are appropriate for these data. (Select all that apply)
A) Overall, speed matters more than octane level.
B) There appears to be interaction between speed and octane level.
C) The effect of speed on mileage is different for different levels of octane.
D) There appears to be no interaction between speed and octane level.
E) The effect of speed on mileage is the same regardless of octane.
F) Overall, octane level matters more than speed.
1. K. Casali conducted a gas mileage study on his well-used four-year-old economy car. He drove a 107-mile course a total of 32 different times in a full factorial experiment with four different speeds (55, 60, 65, 70) and two different levels of octane (87 octane and 90 octane). A table of treatment means and an interaction plot are given below Octane Speed (mph) 8790 Marginal 60 65 70 Marginal34.0 34.35 34.175 35.736.9 36.3 34.5 35.735.1 33.4 33.4 33.4 32.4 31.4 31.9 38 37 36 35 E 34 a 33 32 31 30 29 28 87 90 60 65 70 Speed (mph)Explanation / Answer
D) Speed and octane level are the independent variables here and mileage is the dependent variable. Thus, there is no such interaction between speed and octane level.
The only inference is: For a given Octane level, the mileage decreases with increase in speed.
E) This conclusion is valid.
We see that:
- for speeds 55-65mph, the mileage is higher for Octane 90 and lower for Octane 87.
- At speed 65mph, the mileages are the same for both octane levels.
- But from speeds 65-70mph, the mileage is higher for Octane 87 than Octane 90.
So the effect of speed on mileage is that: As speed increases, mileage decreases for both levels of Octane.
Although the difference in mileage as we increase speed from 55->60->65->70 is not the same both Octane 87 and Octane 90, the overall effect of speed on mileage is not changing with octane level.
For both Octane 87 and 90, the effect of speed on mileage is same i.e as speed increases, mileage decreases.
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