20 The Department of Transportation would like to test the h

20. 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 p-value for this hypothesis test would be?

Solution

Here n>30 so z-test would be used

Mu=10

X-bar=9.5

population SD=3.4 and

a=.10

Z-value would thus be

z= Mu-X-bar/ SE

= 10-9.5/ 3.4/rt10

= 0.5/1.052

=0.4650

The corresponding p-value is the probability of the mean being less than 0.4650= 0.6419 form the distribution if plotted