Question

a car company claims that its new suv gets better gas mileage than its competitors suv. a random sample of 42 of its suvs has a mean gas mileage of 13.9 miles per gallon (mpg). the population standard deviation is known to be 0.6 mpg. a random sample of 36 competitors suvs has a mean gas mileage of 13.5 mpg. the population standard deviation for the competitor is known to be 1.1 mpg. test the companys claim at the 0.01 level of significance. let the car companys suvs be population 1 and let the competitors suvs be population 2. step 3 of 3: draw a conclusion and interpret the decision. answer we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.01 level of significance to support the car companys claim that its new suv has a better mean gas mileage than its competitors suv. we reject the null hypothesis and conclude that there is sufficient evidence at a 0.01 level of significance to support the car companys claim that its new suv has a better mean gas mileage than its competitors suv. we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.01 level of significance to support the car companys claim that its new suv has a better mean gas mileage than its competitors suv. we reject the null hypothesis and conclude that there is insufficient evidence at a 0.01 level of significance to support the car companys claim that its new suv has a better mean gas mileage than its competitors suv.

Explanation:

Step1: Recall hypothesis - testing conclusion rules

In hypothesis - testing, if the p - value is greater than the significance level ($\alpha$), we fail to reject the null hypothesis. If the p - value is less than $\alpha$, we reject the null hypothesis. Here, $\alpha = 0.01$. The null hypothesis $H_0:\mu_1\leq\mu_2$ and the alternative hypothesis $H_1:\mu_1 > \mu_2$ (where $\mu_1$ is the mean gas mileage of the car company's SUVs and $\mu_2$ is the mean gas mileage of competitors' SUVs).

Step2: Analyze the correct conclusion

When we fail to reject the null hypothesis, it means there is insufficient evidence to support the alternative hypothesis. When we reject the null hypothesis, it means there is sufficient evidence to support the alternative hypothesis. Since we want to test if the car company's SUV has a better mean gas mileage (alternative hypothesis), if we fail to reject $H_0$, there is insufficient evidence to support the claim, and if we reject $H_0$, there is sufficient evidence to support the claim.

Answer:

We reject the null hypothesis and conclude that there is sufficient evidence at a 0.01 level of significance to support the car company's claim that its new SUV has a better mean gas mileage than its competitor's SUV.