The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set α = 0.05. Which one of the following statements is true?
A)Because the p- value is less than α, we fail to reject the null hypothesis and conclude that the average age of cars on the road is less than 12 years.
B)Because the p- value is greater than α, we fail to reject the null hypothesis and cannot conclude that the average age of cars on the road is less than 12 years.
C)Because the p- value is less than α, we reject the null hypothesis and conclude that the average age of cars on the road is less than 12 years.
D)Because the p- value is greater than α, we reject the null hypothesis and cannot conclude that the average age of cars on the road is less than 12 years.

Question

Quizplus · Accepted Answer

When the p-value is less than the significance level (α), it indicates that the observed data are inconsistent with the assumption that the null hypothesis is true. Therefore, we reject the null hypothesis. In this context, rejecting the null hypothesis supports the alternative hypothesis that the average age of cars on the road is less than 12 years.

The Department of Transportation Would Like to Test the Hypothesis