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 (alpha = 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 1 of 5: state the null and alternative hypotheses for the test. answer 1 point (h_0:mu_d) (0) (h_a:mu_d) (0)

Explanation:

Step1: Define null and alternative hypotheses

The null hypothesis \(H_0\) is that the mean difference \(\mu_d\) is not positive (no increase in mileage), and the alternative hypothesis \(H_a\) is that the mean difference \(\mu_d\) is positive (increase in mileage).

Step2: Write the hypotheses

The null hypothesis \(H_0:\mu_d\leq0\) and the alternative hypothesis \(H_a:\mu_d > 0\) since we want to test if the gasoline additive significantly increases mileage.

Answer:

\(H_0:\mu_d\leq0\)
\(H_a:\mu_d > 0\)