Durability of car paint, An automobile manufacturer is experimenting with a new type of paint that is supposed to help the car maintain its new-car look

Durability of car paint, An automobile manufacturer is experimenting with a new type of paint that is supposed to help the car maintain its new-car look. The durability of this paint depends on the length of time the car body is in the oven after it has been painted. In the initial experiment, three groups of 10 car bodies each were baked for three different lengths of time—12, 24, and 36 hours—at the standard temperature setting. Then, the paint finish of each of the 30 cars was analyzed to determine a durability rating, y.

(a) Write a quadratic model relating the mean durability, E(y), to the length of baking.

(b) Could a cubic model be fit to the data? Explain.

(c) Suppose the research and development department develops three new types of paint to be tested. Thus, 90 cars are to be tested—30 for each type of paint. Write the complete secondorder model for E(y) as a function of the type of paint and bake time.