Three types of wood (denoted A, B, and C) are being considered for use in a building project. Each type of wood differs in cost, so the builder is interested in keeping costs down as well as in selecting wood that will be strong enough. To determine whether there is a difference between the average strengths of the three types of wood, a random sample of ten beams of each type is selected and their strengths are measured.
a. What hypotheses would you test in such a study? Describe, in words, the parameters that appear in the hypotheses.
b. Suppose an ANOVA test indicates that beams of types A and B are not significantly different in strength from one another, but that both types are significantly stronger than beams of type C. If the builder’s objective is to use as strong a beam as possible, what type of beam should be used?
c. Suppose the ANOVA test does not reveal any significant differences in strength between the three types of beams. If the builder must use one of the three types, which type should be chosen?