The steam explosion of peat renders fermentable carbohydrates that have a number of potentially important industrial uses. A study of the steam explosion process was initiated to determine the optimum conditions for the release of fermentable carbohydrate (Biotechnology and Bioengineering, Feb. 1986). Triplicate samples of peat were treated for .5, 1.0, 2.0, 3.0, and 5.0 minutes at 170°, 200°, and 215°C, in the steam explosion process. Thus, the experiment consists of two factors—temperature at three levels and treatment time at five levels. The accompanying table gives the percentage of carbohydrate solubilized for each of the 3 × 5 = 15 peat samples.

a. What type of experimental design was employed?

b. Explain why the traditional analysis of variance formulas are inappropriate for the analysis of these data.

c. Write a second-order model relating mean amount of carbohydrate solubilized, E(y), to temperature (x₁) and time (x₂).

d. Explain how you could test the hypothesis that the two factors, temperature (x₁) and time (x₂), interact.

e. If you have access to a statistical software package, fit the model and perform the test for interaction.

Transcribed Image Text:

STEAM Time carbohydrate Temperature °C minutes Solubilized % 170 .5 1.3 170 1.0 1.8 170 2.0 3.2 170 3.0 4.9 170 5.0 11.7 200 .5 9.2 200 1.0 17.3 200 2.0 18.1 200 3.0 18.1 200 5.0 18.8 215 .5 12.4 215 1.0 20.4 215 2.0 17.3 215 3.0 16.0 215 5.0 15.3