Question

In 1990, the federal government had issued a new rule that required automakers to meet the average fuel economy standard of greater than 28.0 highway mpg for the 1993 model year. Test whether the 1993 models meet that federal standard. Assume α=0.05.

a) Reject the null hypothesis
b) Fail to reject the null hypothesis
c) Accept the alternative hypothesis
d) Insufficient information provided

Answer 1

To address the student's question, we compare the p-value (0.2578) with the significance level (0.05) in hypothesis testing. Since the p-value is greater than the alpha, we b. fail to reject the null hypothesis, indicating the 1993 models likely meet the federal fuel economy standards.

Step-by-step explanation:

The question you've asked pertains to hypothesis testing in statistics, specifically for testing the average fuel economy of vehicle models against a federal standard. The alpha level (α) given is 0.05. Based on your data, we have a p-value of 0.2578. A key decision rule in hypothesis testing is that if the p-value is less than alpha (α), we reject the null hypothesis. Conversely, if the p-value is greater or equal to alpha, we do not reject the null hypothesis.

Since 0.2578 is greater than 0.05, we would b. fail to reject the null hypothesis. This means there isn't sufficient evidence to say that the 1993 models do not meet the federal standard. Hence, the conclusion drawn should be that there is sufficient evidence to support the claim that the manufacturer's fleet meets the fuel economy standards.

The various scenarios in the examples provided show different hypothesis testing outcomes based on provided p-values in relation to the alpha level. The practice here involves comparing the p-value with the significance level to make a decision on the null hypothesis.