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	22.1	9.3	24.9	25.2	19.4	26.5	18.7	22.4	12.3	22.1
With 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 H0. Round the numerical portion of your answer to three decimal places.

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

Reject Null Hypothesis

or Fail to Reject Null Hypothesis

Answer 1

Number	Without additive	With additive	Difference
	22.1	25.1	-3	0.4624
	9.3	11.6	-2.3	0.0004
	24.9	26.6	-1.7	0.3844
	25.2	28.5	-3.3	0.9604
	19.4	21.4	-2	0.1024
	26.5	28.7	-2.2	0.0144
	18.7	19.5	-0.8	2.3104
	22.4	25.6	-3.2	0.7744
	12.3	14.6	-2.3	0.0004
	22.1	24.5	-2.4	0.0064
Total	202.9	226.1	-23.2	5.016

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = -9.827

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Conclusion :-

Fail to Reject Null Hypothesis