The neighborhood baker has been in business for over 50 years. His famous chocolate birthday cake is his best seller. Within the next few months, the baker will replace his oven-the same oven he's been using since the bakery opened. He will not buy a new oven, however, until he is convinced that the new oven doesn't affect the taste and texture of his famous cake. To help him make a decision, he has hired a statistician, who designs the following experiment.
Two batches of the chocolate birthday cake mix are made: call these Mix A and Mix B. These mixes have all the same ingredients, and the cakes made from them should have the same taste and texture. Each batch makes 10 individual birthday cakes. The individual cakes are randomly distributed among the ovens (see below). After baking, the density of each cake is measured. Here are the results:
Mix A Mix B
Old New Old New
172.4 175.2 174.4 175.3
173.9 175.6 174.5 176.7
175.3 176.4 175.9 178.2
176.1 176.9 176.7 179.1
176.4 177.0 178.7 179.1
Questions:
From the test data, can we determine whether the oven has an effect on the cake's density? The null hypothesis should be: Oven has no effect on density.
To model this problem we could use a linear mixed model, with "Mix" as a random factor and "Oven" as a fixed factor. Would this be a proper way of modeling the problem?
Only two mixes were used in this experiment. Can anything be said about the remaining population of unmade mixes? For example, based on Mixes A and B, is it possible to compute the expected density of an unmade mix, say Mix C? Is it possible to estimate the variance?
Is there a more efficient way to design the experiment to answer the same question? In other words, is there a better way to make use of this data?
What is the power of this test? Is there a formula to compute the power?