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Fuel Efficiency

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The data below summarizes 62 compact automobiles, 54 subcompact automobiles, and 16 two-seater automobiles.

For each vehicle, the engine size (in liters) and the highway fuel efficiency (in miles per gallon) was recorded. Scatterplots of engine size and fuel efficiency for each type of vehicle are given below:

Compact Vehicles

Subcompact Vehicles

Two-Seater Vehicles

In the previous document, lines of best fit were modeling for each type of car. The values of the slopes of those lines are given below, along with the coefficient of determination ($r^{2}$). The coefficient of determination measures what percentage of variability in fuel efficiency can be explained by variability in engine size.

As an example, if $r^{2} = 0.48$, then changing the size of an engine could account for 48% of the resulting changes in highway fuel efficiency, with 52% of the resulting changes in fuel efficiency explicable by other factors besides engine size.

The value of $r$ itself is the correlation coefficient, which in this case is negative for all three vehicles types. The negative values indicate that as engine size increases, fuel efficiency tends to decrease. Values of $r$ that are closer to -1 indicate stronger relationships in a scatterplot, while values of $r$ that are closer to 0 indicate weaker relationships.

Vehicle Type Slope Coefficient of determination ($r^2$)
Compact -3.77 0.62
Subcompact -3.86 0.68
Two Seater -2.48 0.40

The tables below show the means and standard deviations of each vehicle type with respect to engine size and to highway fuel efficiency. The differences between each type of vehicle are statistically significant.

Vehicle Type Mean engine size Standard deviation of engine size Mean fuel efficiency Standard deviation of fuel efficiency Number of vehicles tested
Compact 2.6 L 1.0 L 29.7 mpg 4.8 mpg 62
Subcompact 2.8 L 1.5 L 30.9 mpg 6.9 mpg 54
Two Seater 3.7 L 1.4 L 23.4 mpg 5.5 mpg 16

Consider each of the following statements. Does the information in the three sources support the inference as stated?

Yes

No

Yes

No

On average, two seaters have engines that are at least 25% larger than typical compact or subcompact vehicles.

Yes

No

For two seaters, changing the engine size may result in unpredictable changes to fuel efficiency, since 60% of any differences in fuel efficiency respond to variability in factors other than engine size.

Yes

No

Of the three types of vehicles, two seaters have the strongest relationship between engine size and fuel efficiency.

Yes

No

Two vehicles of the same type have engine sizes of 3.5 L and 4.7 L. The fuel efficiency of those vehicles is 31.2 mpg and 26.6 mpg, respectively. Therefore, of the three possible types of vehicles, it is most likely that these two vehicles are compacts.