Problems

1

• Problems

2

• The tensile strength of concrete produced by 4
  mixer levels is being studied. The data are
• Compute the MS for the mixers and plot the
  means. Is there a difference among them? For the
  greatest tensile strength, which mixer would you
  choose?

3

• For the data in problem 1, compute MS(error) and
  the F-ratio and do the ANOVA table.

4

• 3. Here are the cell and marginal means from an
  experiment.
• According to the ANOVA table, the A and B
  main effects and the AB interaction are all
  significant. If your objective is to minimize
  the response, which values of A and B would you
  select. Explain.

5

• 4. A textile mill has a large number of looms to
  weave its cloth. At random, 3 looms are chosen
  to see if the looms are meeting the standard
  cloth output. The data are
• What type of ANOVA is this? Do the ANOVA to
  see if there is any real variability among the
  looms.

6

• 5. The E(MS) for the A effect is
• (a) What type of factor is this?
• (b) How many factors are in the model?
• (c) How would you set up the F-test?

7

• 6. Because of limited resources, an
  experiment with 4 factors at 2 levels each is
  placed in an 8-run design.
• (a) What kind of design is it?
• (b) What is its generator?
• (c) What is the design resolution?
• (d) List all confounded effects.
• (e) What is the defining relation of the
  complementary fraction?

8

• 7. Three different circuit designs are being
  studied to find the least amount of noise
  present. The data are
• (a) How many replications does this experiment
  have?
• (b) Do the ANOVA.
• (c) Find the best circuit design.

9

• 8. The effects of a 2 x 2 fixed effects
  factorial design are
• A effect 1
• B effect -9
• AB effect -29
• 30.5
• (a) Write the fitted regression model for
  this design.
• (b) Plot the interaction effect.

10

• A factory produces grain refiners in 3 different
  furnaces, each of which has its own unique
  operation characteristics. Each furnace can be
  run at 3 different stirring rates.
• The process engineer knows that stirring
  rate affects the grain size of the product, so he
  decides to run an experiment testing the three
  stirring rates on his 3 furnaces.
• (a) What type of design is this? Why?
• (b) Set up the experiment.

11

• 10. The effect of 5 different ingredients on
  reaction time is being studied. Each batch of
  material is large enough for only 5 runs.
  Moreover, only 5 runs can be made in a day.
  Design the experiment.

12

• 11. The yield of a chemical process is being
  studied using 5 batches of raw material and 5
  acid concentrations, which are nuisance factors.
  
• Two factors are suspected to be important
  standing time (5 levels) and type of catalyst (5
  levels).
• (a) What kind of experiment is this?
• (b) Design the experiment.

13

• 12. The mean results for a completely balanced
  experiment are
• With these cells means, compute orthogonal
  contrasts and their SS for
• (a) High Pressure vs the average of Low and
  Medium Pressure.
• (b) Low Pressure vs Medium Pressure
• (c) Medium Pressure vs High Pressure

14

• 13. A semiconductor engineer is studying the
  effect of lamination temperature (55C and 75C),
  lamination time (10 seconds and 25 seconds),
  lamination pressure (5 tn and 10 tn), and firing
  temperature (1580C and 1620C) on the curvature
  of the substrates produced. He must finish his
  study in one day so he can do only 8 runs. He is
  not very good at experimental design and doesnt
  know how to do it.
• You are his statistical consultant and he asks
  you to design an experiment for him. Design the
  experiment and explain what problems he will have
  after he gets his results.

15

• What do you mean by a completely randomized
  design?

16

• 15. What is the difference between a fixed
  effects model, a random effects model, and a
  mixed model?

17

• 16. What is the purpose of blocking in a design?

18

• 17. What are two ways of dealing with nuisance
  variables in the design we have studied? Why do
  they work?

19

• 18. What is the logic behind decomposition of
  the total SS in ANOVA?

20

• 19. Why is a single-replicate design
  undesirable? How does Cuthbert Daniels idea
  help in this situation?

21

• 20. How do you check model adequacy?