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); thus, a 2 X 4 factorial design with yeast extract at two levels and temperature at four levels was employed. The response variable was the autolysis yield (recorded as a percentage).

a. How many treatments are included in the experiment?

b. An ANOVA found sufficient evidence of factor interaction at α = .05. Interpret this result practically.

c. Give the null and alternative hypotheses for testing the main effects of yeast extract and temperature.

d. Explain why the tests referred to in part c should not be conducted.

e. Multiple comparisons of the four temperature means were conducted for each of the two yeast extracts. Interpret the results, shown as follows:

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Mean yield (%): Temperature (C) 54 45 48 51 Mean yield(%): Temperature (C): 54 51 48 45 Baker's yeast: 41.1 47.5 48.6 50.3 Brewer's yeast: 39.4 47.3 49.2 49.6