Refer to the Electronic Journal of Biotechnology (Dec. 15, 2003) study of two yeast extracts, baker’s yeast and brewer’s yeast, Exercise 13.10. Recall that samples of both yeast extracts were prepared at four different temperatures (45°, 48°, 51°, and 54°C), and the autolysis yield (recorded as a percentage) was measured for each of the yeast–temperature combinations. Thus, a 2 × 4 factorial design was employed, with extract at two levels (baker’s yeast and brewer’s yeast) and temperature at four levels.

a. For this design, give a practical explanation of an interaction between yeast extract and temperature. Illustrate with a graph.

b. Redraw the graph, part a, if no interaction exists. 

c. Write the complete model for mean autolysis yield, E(y), appropriate for analyzing the data.

d. Give the null and alternative hypotheses for testing interaction. Explain how you would conduct this test using regression.

e. An ANOVA resulted in a p-value of .0027 for interaction. Interpret this result, practically, using α = .01.

f. Give the null and alternative hypotheses for testing the main effects of yeast extract and temperature using regression. Explain how you would conduct these main effect tests using regression.

g. Explain why the tests, part f, should not be conducted.    

Data from Exercise 13.10

The Electronic Journal of Biotechnology (Dec. 15, 2003) published an article on a comparison of two yeast extracts, baker’s yeast and brewer’s yeast. Brewer’s yeast is a surplus by-product obtained from a brewery, hence it is less expensive than primary grown baker’s yeast. Samples of both yeast extracts were prepared at four different temperatures (45, 48, 51, and 54°C), and the autolysis yield (recorded as a percentage) was measured for each of the yeast–temperature combinations. The goal of the analysis is to investigate the impact of yeast extract and temperature on mean autolysis yield.