Fuel Consumption and Cars
An investigative reporter believes that certain automobile service stations that offer state vehicle inspections routinely charge for unnecessary repair work. Preliminary data suggest that the cost of the repair work may be related to the age of the car. A random sample of automobiles inspected at these stations was obtained, and the age (in years) along with the cost of the repairs (in dollars) were recorded for each vehicle.
The data are given in the following table
|
Age
|
Repair cost
|
Age
|
Repair cost
|
|
9.1
|
1882
|
3.2
|
17
|
|
3.8
|
193
|
3.3
|
1268
|
|
5.0
|
368
|
6.7
|
1126
|
|
1.7
|
1047
|
3.9
|
646
|
|
1.9
|
315
|
9.7
|
955
|
|
5.3
|
1631
|
2.0
|
801
|
|
5.9
|
652
|
5.4
|
973
|
|
6.4
|
475
|
|
|
a. Find the sample correlation coefficient, and describe the linear relationship.
b. Find the estimated regression line for age (x) and repair cost (y). Conduct an F test for a significant repression, and find the bounds on the p value for this test.
c. Using your results in parts (a) and (b), do you believe the reporter's claim? Justify your answer.