Question

question 2 of 6, step 3 of 3
correct
an auto dealer would like to determine if there is a difference in the braking distance (the number of feet required to go from 60 mph to 0 mph) of two different models of a high - end sedan. six drivers are randomly selected and asked to drive both models and brake once they have reached exactly 60 mph. the distance required to come to a complete halt is then measured in feet. the results of the test are as follows. can the auto dealer conclude that there is a significant difference in the braking distances of the two models? use $alpha = 0.01$. let the braking distances of model a represent population 1 and the braking distances of model b represent population 2.
braking distance of high - end sedans (feet)

driver	1	2	3	4	5	6
model b	150	152	147	146	159	159

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step 3 of 3: make the decision and state the conclusion in terms of the original question.
answer
we fail to reject the null hypothesis and conclude that there is sufficient evidence at an $alpha = 0.01$ level of significance to say that there is a difference in the braking distances of the two models.
we reject the null hypothesis and conclude that there is sufficient evidence at an $alpha = 0.01$ level of significance to say that there is a difference in the braking distances of the two models.
we fail to reject the null hypothesis and conclude that there is insufficient evidence at an $alpha = 0.01$ level of significance to say that there is a difference in the braking distances of the two models.
we reject the null hypothesis and conclude that there is insufficient evidence at an $alpha = 0.01$ level of significance to say that there is a difference in the braking

Explanation:

Step1: Recall hypothesis - testing decision rule

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, $\alpha=0.01$.

Step2: Interpret the result

When we fail to reject the null hypothesis, it means there is insufficient evidence to support the alternative hypothesis. In the context of this problem, the null hypothesis is that there is no difference in the braking distances of the two models, and the alternative hypothesis is that there is a difference. Since we fail to reject the null hypothesis at $\alpha = 0.01$, we conclude that there is insufficient evidence at the $\alpha=0.01$ level of significance to say that there is a difference in the braking distances of the two models.

Answer:

We fail to reject the null hypothesis and conclude that there is insufficient evidence at an $\alpha = 0.01$ level of significance to say that there is a difference in the braking distances of the two models.