The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 10 years. A random sample of 50 cars had an average age of 9.5 years. It is believed that the population standard deviation for the age of cars is 3.4 years. The Department of Transportation would like to set = 0.10. The critical value for this hypothesis test would be .

0.1492

Step-by-step explanation:

Mean (m) = 9.5

Standard deviation (sd) = 3.4

Number of observations (n) = 50

Computing the test statistic :

X = 10

Z = (x - m) / standard error

Standard Error = sd/sqrt(n)

Z = (x - m) / (sd/sqrt(n))

Z = (10 - 9.5) / (3.4/sqrt(50))

Z = 0.5 / 0.4808326

Z = 1.0398 = 1.04

Using a P-value calculator, we can obtain the critical value with α = 0.10, hence, the critical value = 0.14917

= 0.1492