A petroleum engineer wants to know whether a certain fuel additive improves a car's gas mileage. To decide, the engineer records the gas mileages (in miles per gallon) of 33 randomly selected cars with and without the fuel additive. The table shows the results. At \(\alpha=0.10\), can the engineer conclude that the gas mileage is improved?

Perform the Wilcoxon signed-rank test using the test statistic for \(n>30\).

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Car 1 2 3 4 5 6 7 8 9 9 10 11 Without additive 36.4 36.4 36.6 36.6 36.8 36.9 37.0 37.1 37.2 37.2 36.7 36.7 36.9 37.0 37.5 38.0 38.1 38.4 38.7 38.8 38.9 36.3 With additive Car 12 13 14 15 16 17 18 19 20 21 22 Without additive 37.5 37.6 37.8 37.9 37.9 38.1 38.4 40.2 40.5 40.9 35.0 With additive 38.9 39.0 39.1 39.4 39.4 39.5 39.8 40.0 40.0 40.1 36.3 Car 23 24 25 26 27 28 29 30 31 32 33 Without additive 32.7 33.6 34.2 35.1 35.2 35.3 35.5 35.9 36.0 36.1 37.2 With additive 32.8 34.2 34.7 34.9 34.9 35.3 35.9 36.4 36.6 36.6 38.3