Question

A major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage? Let d = (gas mileage with additive)-(gas mileage without additive). Use a significance level of a = 0.1 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive. Car Without additive With additive 1 11.7 14.4 2 26 27.1 3 20.2 21.3 4 22.2 23.4 5 16.2 17.4 6 16.4 16.6 7 21.7 22.2 8 26 26.9 9 27.4 30.1 10 18.5 19.8 Copy Data Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to two decimal places.

Answer 1

The statistic software output for this problem is:

Paired T hypothesis test: HDH-H Mean of the difference between With and Without Ho HD 0 HA HD 0 Hypothesis test results: Difference Mean Std. Err. DF P-value T-Stat With Without 1.29 0.25882212 9 4.9841181 0.0004

Standard deviation = 0.25882212 * $\sqrt$ 10 = 0.82