A Chemist plans to investigate the effects of four types of catalyst (???) and three types of reagents (??) on the rate of a chemical reaction. Suppose that the amount of each type of catalyst and reagent, if decided to add, is fixed. Also, at most one type of catalyst and one type of reagent can be added simultaneously.
Before planning the experiment she seeks your advice on how to run the experiment. She has written to you as follows:
"I intend to study the catalysts first and then the reagents. However, I am restricted to fewer than or equal to 50 observations in total. In the first experiment I could use 6 replicates of each catalyst and in the second experiment I could use 8 replicates of each reagent. Then, I have 4*6 + 3*8 = 48
observations from this experimental plan. Alternatively, I could use 7 replicates of each catalyst in the first experiment, and 6 replicates of each reagent in the second experiment. Then, I totally use 4*7 + 3*6 = 46 observations from this experimental plan. Which of the two experimental plans would be best?"
You have made an appointment to see her in order to discuss this. Make clear notes on the most important points to discuss with her at your meeting. Explain the statistical motives for discussing these points. You do not need to restrict the discussion to her specific question and you should include a preliminary recommendation of a plan for the experiment (please try to limit your answer within 500 words).