An engineer and a material scientist are interested in a process for making a synthetic material. Contamination of the material during production is thought to be a real possibility. To find manufacturing conditions that produce minimal contamination, they select three different curing times and two different coating conditions (none versus some) for producing the material. Suppose two pieces of the synthetic material are produced for each combination of time and coating condition. The order of production is randomized and the raw material is randomly assigned to combinations of time and coating. The amount of iron (an important contaminant) in the final product is measured.

(a) What type of (designed) experiment is this?

(b) How many treatment combinations are there in this experiment?

(c) To what future production circumstances can conclusions based on this experiment be extended?

(d) Write a model equation for this experiment. Let "time" be Factor A and "coating condition" be Factor B. Say what each model term means, both in mathematical terms and in the context of the physical experiment.

(e) What are the degrees of freedom for the estimated variance in response (for pieces made under a given set of process conditions)?

(f) How many factors are there in this experiment? Identify the number of levels for all factors.

(g) Write your answer to (b) as I × J ×··· , in terms of the number of levels you gave in answer to (f).