Modern Ice Creams are Not Simple Recipes

Assignment Task

Modern ice creams are not simple recipes. Many use some type of gum to enhance texture, and a noncream protein source (for example, whey protein solids). A food scientist is trying to determine how types of gum and protein added change a sensory rating of the ice cream. She runs a five by five factorial with two replications using five gum types and five protein sources. Unfortunately, six of the units did not freeze properly, and these units were not rated. Ratings for the other units are given below (higher numbers are better)

(a) Is it a balanced design?

(b) Based on R output, what is your final model? Explain briefly why. Which R output did you use?

(c) Based on R output, test if there is an interaction effect between two factors. Write the null and alternative hypothesis, decision, and conclusion. 

2. Consider a four-factor model with A and B fixed, each with three levels. Factors C and D are random with two levels each. B nests in A, D nests in C, and all other combinations cross. There is a total of 72 observations.

(a) Draw the Hasse diagram for this model.

(b) Write down the corresponding model.

(c) Fill the blanks in the ANOVA table,

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