A petroleum engineer claims that a fuel additive improves gas mileage. The table shows the gas mileages (in miles per gallon) of 32 randomly selected cars measured with and without the fuel additive. Test the petroleum engineer's claim at \(\alpha=0.05\).

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 10 11 Without additive 34.0 34.2 34.4 34.4 34.6 34.8 35.6 35.7 30.2 31.6 32.3 36.6 36.7 37.2 37.2 37.3 37.4 37.6 37.7 34.2 34.9 34.9 With additive Car 12 13 14 15 16 17 18 19 20 20 21 22 Without additive 33.0 33.1 33.7 33.7 33.8 35.7 36.1 36.1 36.6 36.6 36.8 With additive 34.9 35.7 36.0 36.2 36.5 37.8 38.1 38.2 38.3 38.3 38.7 Car 23 24 25 26 27 28 29 30 31 32 Without additive 37.1 37.1 37.2 37.9 37.9 38.0 38.0 38.4 38.8 42.1 With additive 38.8 38.9 39.1 39.1 39.2 39.4 39.8 40.3 40.8 43.2