1. In a chemical plant there are four "identical" reactors that can be run in parallel. Raw materials from a common source are fed continuously to the reactors. The standard operating temperature of these reactors is 120°C, but there is a proposal to use 180°C. It is claimed that this increased temperature should improve the yield of the process.

Set up an experimental design over a four-day period to test the hypothesis that the increased temperature will improve the yield, using temperature levels at 120, 140, 160 and 180°C.

Please note that all reactors can be operated each day but each can only be operated at one temperature on a given day. What would be the best fitting design for this situation? Why? Create the design matrix and give exact and specific instructions to the plant operator what to do each day. She will run the experiments exactly as instructed.

2. Pick any one of the following superstitions and design an experiment to test if the superstition holds. To run your experiment, you have at most one month, maximum $1000 and under no circumstances you can do more than 100 runs altogether.

Specify the following:

a) Superstition selected? Problem statement?

b) Factor(s)? Levels?

c) Response Variable?

d) Is there a need to use blocks? If yes, what factor would be the blocking one?

e) Total number of runs?

f) Approximate time frame?

g) Approximate cost? (1 pt)

h) Best design method? (e.g. 2^3 design with a block, a 3^2 resolution III fractional factorial design, graeco-latin square, etc. ) Why?

• An apple a day keeps the doctor away.
• Eating chocolate causes zits.
• Shaving your legs makes the hair grow back more densely.
• A knife placed under the bed during childbirth will ease the pain of labor.
• Drinking coffee will stunt a child's growth.

3. Fill out the tables below with + and - signs for a 2³ factorial design example with 2 replicates.

4. Your best friend wants to improve his golf game and wants to maximize the distance of a hit. He designs an experiment where he uses the following: Driver 1 is the Calloway Big Bertha Diablo, Driver 2 is the Adams Speedline Fast 10, Driver 3 is the Taylormade Rll, Ball 1 is the Top Flite D2 Distance, Ball 2 is the Titliest Pro V1, and Ball 3 is the Bridgestone E5.

Assuming that he collected the data the right way following design of experiments principles (randomized order, controlled all the controllable factors, etc.), he hands you the following data table where he recorded his distances:

Analyze the data and make a recommendation about the best driver and ball to use to improve his game. In case he does not believe you, support your recommendation with the proper main effects and interaction effects plot as well.