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. 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.

Explanation:

Step1: Identify the test type

This is a one - tailed paired t - test. The degrees of freedom is $n - 1$, where $n=10$, so $df=10 - 1 = 9$.

Step2: Find the critical value

For a one - tailed paired t - test with $\alpha = 0.05$ and $df = 9$, looking up in the t - distribution table, the critical value $t_{\alpha,df}=t_{0.05,9}=1.833$.

Step3: Determine the decision rule

Since we are testing if the additive increases mileage (right - tailed test), we reject $H_0$ if $t>1.833$.

Answer:

Reject $H_0$ if $t>1.833$