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# Rank Correlation for Car Fuel Consumption

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Car Fuel Consumption

Listed below are the highway fuel consumption amounts (in mi/gal) from cars in three different categories. Use a 0.05 signifiacance level to test the claim that the different car categories have the same median highway fuel consumption. Based on the results, does the number of cylinders appear to affect highway fuel consumption?

Four cylinder

31 30 32 30 32 34 32 34 32 29 32 38 31

Six cylinder

26 29 29 27 27 25 25 30 37 32 31 27

Eight cylinder

25 25 25 27 25 25 25

(i) Test statistic H =

(ii) Critical value &#935;^2 =

(iii) Conclusion on H0:

(iv) Interpret the results according to the problem.

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The expert examines Rank correlation for Car Fuel Consumption.

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Step by Step Solution

We use Kruskal-Wallis test to test the following hypothesis.

Null Hypothesis :

H0 : Different car categories have the same median high way fuel consumption.

Alternative Hypothesis:

Ha : At least one of the car categories have different median high way fuel consumption.

Following table shows the given fuel consumption values of the three categories including the combined rank for each value.

S.No. Four Cylinder Six Cylinder Eight Cylinder
mi./gal Rank mi./gal Rank mi./gal Rank
1 31 21 26 9 25 4.5
2 30 18 29 15 25 4.5
3 32 25.5 29 15 25 4.5
4 30 18 27 11.5 27 11.5
5 32 25.5 27 11.5 25 4.5
6 34 29.5 25 4.5 25 4.5
7 32 25.5 25 4.5 25 4.5
8 34 29.5 30 18
9 32 25.5 37 31
10 29 15 32 25.5
11 32 25.5 31 21
12 38 32 27 11.5
13 31 21
Total R1 = 311.5 R2 = 178 R3 = 38.5
Average 23.96 14.83 5.50

We see that the ...

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