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
Without additive	17.5	11.2	15.2	2727	25.2	15.7	20	9.1	11.5	28.4
With additive	18	14	16.9	27.427.4	26.4	17.9	22.5	11.4	13.8	28.7

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 H₀. 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 want to check that the gasoline additive does significantly increase mileage.
For this we consider sample 1 as gas mileage with additive and sample 2 as gas mileage without additive

For standard deviation we consider the difference as sample data below

The standard deviation of the paired differences = 0.95

we conclude that the gasoline additive significantly increase mileage.

PL??