4. Consider performing experiments to determine the eect of popcorn brand, power level, and time on the percentage of edible popcorn (unpopped or burnt is not edible) kernels made in a microwave oven. The object is to maximize the proportion of edible kernels. Start with 1 3 cup of kernels and do pilot experiments to determine the range of the factors you would like to study and an estimate of the standard deviation of replicates made under the same conditions.

(a) What is the experimental unit for this experiment?

(b) Determine how many replicates will be required to detect a maximum dierence in marginal (main eect) means of 0.25.

(c) Determine the number of levels of the factors you would like to study, and create a randomized list of the experiments for a factorial design.

(d) Actually perform the experiments and collect the data.

(e) Analyze the data. Partition any signicant eects of power level and time into orthogonal polynomial contrasts. Interpret the results, and determine the optimum combination of factor levels from among those you tested.

(f) How many experiments would it have taken to get the same power for main eects using a vary one-factor-at-a-time plan? Would you detect the same optimum using the vary one-factor-at-a-time plan?