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 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
W/O Additive	22.1	9.3	24.9	25.2	19.4	26.5	18.7	22.4	12.3	22.1
W/ Additive	25.1	11.6	26.6	28.5	21.4	28.7	19.5	25.6	14.6	24.5

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to two decimal places.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

Answer 1

We use matched pairs comparisons test to test the hypothesis.

Step 1: Null hypothesis- There is no effect of gasoline additive on mileage i.e

Alternative hypothesis- There is a significant increase in mileage by adding gasoline additive i.e

Step 2: The mileage difference values (d) are 3, 2.3, 1.7, 3.3, 2, 2.2, 0.8, 3.2, 2.3, 2.4

Standard deviation

From the above d values, =  2.32, n = 10

By substituting, we get = 0.75

Step 3: The test statistic for the matched pairs comparisons test is given by

By substituting, we get

Therefore test statistic is 9.782

Step 4: Since this is an upper tailed test, we reject the null hypothesis if t > 1.833, the value of for 10 - 1 = 9 degrees of freedom.

Step 5: Since t = 9.782 is greater than 1.833, we reject the null hypothesis. We can conclude that the addition of gasoline additive has shown a significant increase in mileage