Reference no: EM13903888

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.

Run Order	Completely Randomized Factor A     Factor B			Run Order	Randomized Block   Factor A       Factor B			Run Order	Repeated   Factor A	Measures   Factor B
1				1				1
2				2				2
3				3				3
4				4				4
5				5				5
6				6				6
7				7				7
8				8				8
9				9				9
10				10				10
11				11				11
12				12				12
13				13				13
14				14				14
15				15				15
16				16				16

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:

Combination	Distance	Distance	Distance	Distance	Distance	Distance	Distance	Distance	Distance	Distance
Driver 1 Ball 1	255	260	250	265	263	270	256	272	263	264
Driver 1 Ball 2	268	274	275	277	285	271	279	286	267	273
Driver 1 Ball 3	270	275	278	279	265	273	282	275	277	265
Driver 2 Ball 1	260	265	263	270	266	262	266	271	265	260
Driver 2 Ball 2	271	278	276	271	277	281	275	277	273	276
Driver 2 Ball 3	265	268	284	270	267	271	270	275	280	258
Driver 3 Ball 1	270	275	265	278	280	283	270	265	275	281
Driver 3 Ball 2	280	284	289	292	292	284	279	287	281	288
Driver 3 Ball 3	275	271	279	271	271	278	264	275	222	263

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.