Decide which Wilcoxon test (i.e. the Wilcoxon signed-ranks test or Wilcoxon Rank

Question

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

5. Fuel Additive. A researcher claims that using a fuel additive improves the gas mileage for cars. 10 cars were randomly selected. The gas mileage was measured for each car (miles per gallon). Then the same cars were subjected to a second test after fuel additive was mixed with the fuel. The gas mileage for the cars are shown in the table below. At a 0.05, can you support the researcher's claim Car 1 2 4 6 7 8 9 10 Before 28 31 37 34 29 32 36 33 38 27 After 29 31 39 34 30 32 35 36 38 28

Explanation / Answer

By using R software we can solve this qustion.

First, enter data into excel.

Claim: Using a fuel additive improves the gas mileage for cars.

H0: The median difference is zero Vs

H1: The median difference is positive

=0.05

R codes and output

> wilcox.test(Before,After,paired = TRUE)

   Wilcoxon signed rank test with continuity correction

data: Before and After
V = 2.5, p-value = 0.1058
alternative hypothesis: true location shift is not equal to 0

P-value > 0.05 we fail to reject null hypothesis.

Conclusion:Using a fuel additive does not improves the gas mileage for cars.

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