Commercially produced ice cream is made from a mixture of ingredients:

• A minimum of 10% milk fat

• 9– 12% milk solids: this component, also known as the serum solids, contains the proteins (caseins and whey proteins) and carbohydrates (lactose) found in milk

• 12– 16% sweeteners: usually a combination of sucrose and/ or glucose- based corn syrup sweeteners

• 0.2– 0.5% stabilizers and emulsifiers— e. g., agar or carrageenan extracted from seaweed

• 55%– 64% water, which comes from milk solids or other ingredients

Air is incorporated with the above ingredients during the mixing process. Less- expensive ice creams contain lower- quality ingredients, and more air is incorporated during the mixing process. The finest ice creams have between 3% and 15% air. Because most ice cream is sold by volume, it is economically advantageous for producers to reduce the density of the product in order to cut costs. A food scientist is investigating how varying the amounts of the above ingredients impacts the sensory rating of the final product. The scientist decides to use three levels of milk fat: 10%, 12%, 15%; three amounts of air: 5%, 10%, 15%; and two levels of sweeteners: 12%, 16%. Three replications of each of the formulations were produced and the sensory ratings (0– 40) obtained; a higher number implies a more favorable sensory rating. The data are given here.

a. Identify the design and treatment structure for this study.

b. Write a model for this study, identifying all the terms in the model.

c. For each of the two levels of sweetener, draw profile plots of the effects of the percentages of air and milk fat on the sensory rating of ice cream.

d. From the profile plots, does there appear to be a three- way interaction among the effects of the percentages of sweetener, air, and milk fat on the mean sensory ratings?

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