A building materials engineer is experimenting with three different cement mixes—dry, damp, and wet—for laying concrete. Since the compressive strength of a concrete slab varies as a function of hardening time and cement mix, the following main effects model is proposed:

E(y) = β₀ + β₁x₁ + β₂x₂ + β₃x₃

where

Dry cement is the base level.

a. What hypothesis would you test to determine whether mean compressive strength differs for the three cement mixes?

b. Using data collected for a sample of 50 batches of concrete, the main effects model is fit, with the result SSE = 140.5. Then the reduced model E(y) = β₀ + β₁x₁ is fit to the same data, with the result SSE = 183.2. Test the hypothesis you formulated in part a. Use α = .05.

c. Explain how you would test the hypothesis that the slope of the linear relationship between mean compressive strength E(y) and hardening time x₁ varies according to type of cement mix.

d. Write a second-order model that allows different response
curves for the three types of cement mixes.

e. Explain how you would test the hypothesis that the three response curves have the same shape, but different y-intercepts.

Transcribed Image Text:

y = Compressive strength (thousands of pounds per square inch) Hardening time of cement mix (days) %3! Si if damp cement lo if not X2 Si if wet cement = Er lo if not