Does the fuel additive raise mpg? (one-sided paired test)

Question

A fuel additive is tested on the same 8 cars, each driven a fixed route with and without the additive. For each car, compute the mileage gain (with minus without, in mpg). The gains have a mean of 2.5 mpg and a sample standard deviation of 2.0 mpg. The maker claims the additive can only help, so test one-sided.

Run a one-sided paired t-test at the 5% level: does the additive improve mileage? Report the t-statistic.

Accepted Answer

Paired data, so use the differences di with a one-sample t-test on 8 - 1 = 7 degrees of freedom. Because the claim is directional (improvement only), use a one-sided (upper-tail) test. Hypotheses: H0: \mud = 0 versus H1: \mud 0. Standard error: 	ext{SE} = \frac{sd}{\sqrt{n}} = \frac{2.0}{\sqrt{8}} = \frac{2.0}{2.828} = 0.7071 	ext{ mpg}. Test statistic: t = \frac{2.5}{0.7071} = 3.54. The one-sided 5% critical value for 7 degrees of freedom is t{0.05,\,7} = 1.895. Since 3.54 1.895, reject H0. The one-sided p-value is about 0.005. Conclusion: strong evidence the additive improves mileage, by …

Does the fuel additive raise mpg? (one-sided paired test)

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