A spoilage-retarding ingredient is added in brewing beer. To determine the extent to which the taste of the beer is affected by the amount of this ingredient added to each batch, and how such taste changes might depend on the age of the beer, a \(3 \times 4\) factorial experiment in two replications was designed. The taste of the beer was rated on a scale of \(0,1,2\), or 3 ( 3 being the most desirable) by a panel of trained experts, who reported the following mean ratings:

Interpret the results of this experiment.

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Amount of Ingredient Aging Period Mean Ratings (grams per batch) (weeks) Rep. I Rep. 2 222333444555 2 2 3 4 5 246246246246 2.1 1.6 2.6 1.9 2.9 2.4 1.4 1.7 1.9 2.2 2.3 2.7 0.5 0.9 1.2 0.8 1.7 1.4 1.0 1.6 2.2 1.3 2.3 2.1