text: # maths-help-need-in-24-hours
  
  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? (1 pt)
  
  b)      Factor(s)? Levels? (1 pt)
  
  c)      Response Variable? (1 pt)
  
  d)     Is there a need to use blocks? If yes, what factor would be the blocking one? (1 pt)
  
  e)      Total number of runs? (1 pt)
  
  f)       Approximate time frame? (1 pt)
  
  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? (3 pts)
  
  • 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
  
  Q4)
  
  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
  
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  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.
  
  -15-