Refer to Exercise 18.33.
a. Do the necessary conditions for testing hypotheses and constructing confidence intervals appear to be satisfied? Justify your answers using the residuals from fitting the model from Exercise 18.33.
b. Construct an ANOVA table for this experiment. Make sure to include expected mean squares and the p-values for the F tests.
c. At the .05 level, which main effects and interaction effects are significant? Justify your answer by including the relevant p-values.
d. What are your overall conclusions about the impact of the four sweeteners and the blending times on the average texture scores?
A group of researchers at a company that produces a leading brand of ice cream design an experiment to evaluate the impact of several artificial sweeteners on the texture of the product. It is well known that replacing natural sweeteners with artificial sweeteners in ice cream can result in a product that is has an unappealing texture. A proposed method to overcome this problem is to increase the blending time in the production process. The researchers decided to use four types of sweeteners: a natural sweetener (control), Aspartame, Saccharin, and Sucralose. Twelve containers of ice cream were made, 3 for each of the four types of sweeteners, with the type of sweetener randomly assigned to the containers. Each of the 12 containers of ice cream was then split into four portions. The four portions were then randomly assigned to one of four blending times: 1 minute, 2 minutes, 5 minutes, and 8 minutes. At the end of the specified blending period, the ice cream was assigned a texture score. The researchers were particularly interested in the impact of the four sweeteners and the blending times on the average texture scores.
a. What type of randomization was utilized in this experiment (completely randomized design, randomized complete block design, Latin square design, etc.)?
b. What type of treatment structure was used (single factor, crossed factors, nested factors, etc.)?
c. Identify each of the factors as being fixed or random.
d. Describe the experimental units for each factor and the measurement units.
e. Write a statistical model for this experiment, and include all necessary conditions on the model parameters and variables.
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