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 = 0.05 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 25.5 27.7 19.5 22.4 9.9 21.1 13.1 26.7 20.6 24.9 With additive 25.7 28.6 21.4 25.7 13.4 21.7 14.630 23 26.5

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

Ho: μd (=,≠,<,>,≤,≥) 0

Ha: μd (=,≠,<,>,≤,≥) 0

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.

Reject Ho if (t, I t I) (<,>) _____

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

Reject Null Hypothesis Fail to Reject Null Hypothesis

Answer 1

d=(with additive) without additive d: 0.2 0.9 1.9 3.3 3.5 oob 1.5 3.3 2.4 azad = 1902 sa=Salzd2 (&d)2) = √5 (49.42-(19.2/2) = [1.18 lo Step1 : Ha Stepy: Ho: Md =0 (VS) Mdzo Step2 : Standard deviation of paired differences (S-1118 Step3 : The test statistic tastalla - 1.9250 3.373 Sada (my a 2005 significance land (&f=n-1=9) Rejeet Ho it t > 1.833 Reject hall Hypothesis Steps