Question: Soybean sausage. A food technologist, testing storage capabilities for a newly developed type of imitation sausage made from soybeans, conducted an experiment to test the effects of humidity level (factor \(A\) ) and temperature level (factor \(B\) ) in the freezer compartment on color change in the sausage. Three humidity levels and four temperature levels were considered. Five hundred sausages were stored at each of the 12 humidity-temperature combinations for 90 days. At the end of the storage period, the researcher determined the proportion of sausages for each humidity-temperature combination that exhibited color changes. The researcher transformed the data by means of the arcsine transformation (18.24) to stabilize the variances. The transformed data \(\dot{Y}=2 \arcsin \sqrt{Y}\) follow.

1. Plot the data in the format of Figure 20.1. Does it appear that interaction effects are present? Does it appear that factor \(A\) and factor \(B\) main effects are present? Discuss.
2. Conduct separate tests for humidity and temperature main effects. In each test, use level of significance \(01=.025\) and state the alternatives, decision rule, and conclusion. What is the \(\mathrm{P}\) -value for each test?
3. Obtain confidence intervals for :
   \(D_{.1}=\mu_{.2}-\mu_{-1}, D_{2}=\mu_{.3}-\mu_{.2}\), and \(D_{3}=\mu_{.4}-\mu_{.3}\). Use the Bonferroni procedure with a 95 percent family confidence coefficient. State your findings.
4. Conduct the Tukey test for additivity; use \(\alpha=.005\). State the alternatives, decision rule, and conclusion. If the additive model is not appropriate, what might you do?

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