Question

Decide which Wilcoxon test (i.e. the Wilcoxon signed-ranks test or Wilcoxon Rank Sums test) should be used. Then test the claim.

Exercise 5. Fuel octane. A researcher wants to know if the octane level in gasoline affects car mileage. 12 randomly selected cars are tested. 5 gallons of 87-octane gas is put in the tank and then the car is run until it runs out of gas. The same cars are then tested in the same way, except that 5 gallons of 92-octane gas is put in the tank. The data for both octane levels is summarized in the table below. At a 0.05, can you support the claim that fuel octane does increase car milage? 2 3 18.0 23.2 31.5 24.9 18.5 23.1 31.9 26.7 5 6 7 1112 8 Car 1 4 10 24.1 25.1 23.4 23.119.0 26.8 31.8 20.2 | 27.4 87-octane 23.5 19.526.2 | 30.7 | 21.5 28.3 92-0ctane 22.8

Answer 1

Since the samples are related ,. We use Wilcoxon signed ranks test while Wilcoxon rank sum test is used for independent samples

Null Hypothesis H₀: The medians of 2 fuel octanes are identical

Alternative Hypothesis,H_a: The median of 92 octane fuel is more than median than 87 fuel octane

Test procedure :

• Open SPSS and enter the data
• Go to analyse , then non parametric tests , then legacy and select 2 related samples
• Transfer the variables to the respective boxes and click ok to get the output

Z= - 1.178

p value is 0.1195

Since p value is more than .05, we accept H₀ and conclude that fuel octane increases car mileage