An automotive manufacture claims the mean price of a small SUV is 27,103. If a hypothesis test is performed, how should you interpret a decision that
(a) Reject the null hypothesis
(b) Fails to reject the null hypothesis
Solution
(a) Begin by determining the claim of the hypothesis test.
The claim is µ = 27,103.
Next determine whether the claim is the null hypothesis or the alternative hypothesis. The null hypothesis, 
, is a statistical hypothesis that contain a statement of equality, whereas the alternative hypothesis, 
, contain a statement of strict inequality.
Since the claim contains a statement of equality, µ = 27,103, it is the null hypothesis.
When a null hypothesis is rejected, there is sufficient evidence, that the null hypothesis is false and enough evidence to support the alternative hypothesis. Thus, since the claim is the null hypothesis, there is enough evidence to reject the claim that the mean price of a small SUV is 27,103.
(b) As in part (a), begin by determining the claim of the hypothesis test and determine whether it is the null or alternative hypothesis. Note that you have already found that the claim of the hypothesis test is µ = 27,103 and that it is the null hypothesis.
When you fail to reject the null hypothesis, there is insufficient evidence that the null hypothesis is false and not enough evidence to support the alternative hypothesis. Thus, since the claim is the null hypothesis, there is not enough evidence to reject the claim that the mean price of a small SUV is 27,103.