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) d = (gas mileage with additive) − (gas mileage without additive) . Use a significance level of α=0.05 α = 0.05 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive. Car 1 2 3 4 5 6 7 8 9 10 Without additive 21.1 21.1 16.7 16.7 25.9 25.9 19.6 19.6 15.5 15.5 23 23 17.2 17.2 9.8 9.8 25.8 25.8 19.6 19.6 With additive 24.2 24.2 17 17 27.2 27.2 19.9 19.9 16.7 16.7 23.7 23.7 19.6 19.6 13.1 13.1 28.6 28.6 22.5

a) State the null and alternative hypothesis for the test

b) Find the value of the standard deviation of the paired differences. Round to 2 decimals.

c) Compute the value of the test statistic. Round to 4 decimals.

d) Determine the decision rule for rejecting the null hypothesis (round to 3 decimals) and Make a decision for the hypothesis test.

Answer 1