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. The conclusion for this hypothesis test would be that because the test statistic is _________.
A)more than the critical value, we can conclude that the average age of cars on the road is less
B)less than the critical value, we cannot conclude that the average age of cars on the road is less than 12 years
C)less than the critical value, we can conclude that the average age of cars on the road is less than 12 years
D)more than the critical value, we cannot conclude that the average age of cars on the road is less than 12 years

Question

Quizplus · Accepted Answer

The test statistic, calculated using the sample mean, population standard deviation, and sample size, would be compared to the critical value from the Z-distribution (since population standard deviation is known) for a one-tailed test at α = 0.05. If the test statistic is less than the critical value, it indicates that the sample mean is significantly lower than the hypothesized mean, leading to the conclusion that the average age of cars on the road is less than 12 years.

The Department of Transportation Would Like to Test the Hypothesis