STATISTICS 402 - Assignment 4
Due March 2, 2012
1. Oleoresin, which is used to make turpentine and rosin, is obtained from pine trees by cutting
a hole in the bark and collecting the resin that seeps out. We want to design an experiment to
see if the shape of the hole (circle, triangle, square or pentagon) has an effect on the amount
of resin obtained. A second factor, the application of an acid (no acid or acid) to the hole is to
be investigated in a two factor completely randomized experiment.
a) What is the response?
b) What is the experimental material?
c) The experimenter will use factorial crossing to create the treatment combinations. How
many treatment combinations will there be in the experiment? List all the treatment
combinations.
d) The experimenter would like to be able to detect a difference in treatment means of 1.6
standard deviations with Alpha = 0.05 and Beta = 0.10. How many experimental units
will the experimenter need?
e) With this number of units, what size difference in factor level means can be detected
when Alpha=0.05 and Beta=0.10?
f) Because of budget constraints, only 6 units are available for each treatment combination.
How does this choice affect the size of the detectable difference in treatment means? in
factor level means? Use Alpha=0.05 and Beta=0.10.
Pine plantations are easily differentiated from natural pine forests due to the regular spacing
of pines in rows.
g) Explain how you would randomly select units for the experiment from a plantation
consisting of 200 rows with each row having 50 pine trees. Remember the budget
constraints in f).
h) Explain how you would randomly assign treatments to the units you selected in g).
Include a table that indicates the random assignment of treatments to units. Remember
the budget constraints in f).
2. An experiment is performed on individuals with elevated serum cholesterol. The individuals
will be treated with one of two drugs, Lipitor® or Zocor®. The dosage will also be varied
(None, Low and High). A dosage of “None” is a placebo pill that looks like the drug but
contains none of the active ingredient. At the beginning of the study the total cholesterol for
each individual is determined. At the end of three months the total cholesterol for each
individual is determined again. The change in cholesterol is calculated (Three Month Value –
Beginning Value) so that a negative change means the total cholesterol has decreased.
a) What is the response?
b) What are the conditions?
c) What are the experimental units?
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d) Why is random assignment of treatments to the experimental units in this experiment
important? Be specific and be sure your answer deals with this experiment.
Placebo (None)
Low
High
Lipitor®
–13 –26 –19 –25 –9 –23
–25 31 25 –18 –22 9
–5 –23 –8 23 –5 36
–12 –46 –6 –23 –41 –40
–32 –65 –8 –59 –26 27
–28 –34 –52 –40 –1 –44
–8 –12 –39 –27 –32 –13
–18 –55 13 6 –43 –37
–56 –61 –3 –49 –58 –84
Zocor®
27 6 –17 –19 –24 –22
–19 –10 –34 11 –16 –4
–19 –16 19 14 14 18
–25 23 –48 –27 –79 –61
6 –38 –27 –21 18 –40
–46 –17 –33 –42 –23 –32
–79 –29 –38 –32 –36 –22
–17 –12 –102 –41 –87 –64
–16 –39 –51 –36 –48 –20
e) Give the full model for these data. Be sure to define all the terms in the model within the
context of the problem.
f) Test the hypothesis that all the treatment effects are zero against the alternative that at
least one is not zero. Be sure to give an appropriate null and alternative hypothesis using
the notation from your answer to e). Report the value of the appropriate test statistic, Pvalue, decision, reason for the decision and a conclusion within the context of the
problem.
g) Test the hypothesis that all the drug effects are zero against the alternative that at least
one is not zero. Be sure to give an appropriate null and alternative hypothesis using the
notation from your answer to e). Report the value of the appropriate test statistic, Pvalue, decision, reason for the decision and a conclusion within the context of the
problem.
h) Where are the statistically significant differences in drug sample means? Support you
answer with an appropriate multiple comparison procedure.
i) Test the hypothesis that all the dosages of drug effects are zero against the alternative that
at least one is not zero. Be sure to give an appropriate null and alternative hypothesis
using the notation from your answer to e). Report the value of the appropriate test
statistic, P-value, decision, reason for the decision and a conclusion within the context of
the problem.
j) Where are the statistically significant differences in dosage level sample means? Support
you answer with an appropriate multiple comparison procedure.
k) Are there any interaction effects that are different from zero? Be sure to give an
appropriate null and alternative hypothesis using the notation from your answer to e).
Report the value of the appropriate test statistic, P-value, decision, reason for the decision
and a conclusion within the context of the problem.
l) Construct an interaction plot. Comment on the plot and what it tells you about the
interaction between the two factors. Be specific and be sure your answer deals with this
experiment.
m) Construct plots of residuals versus the levels of the two factors. Describe the plots and
indicate what this tells you about the Fisher conditions necessary for the analysis of
variance.
n) Construct plots of the distribution of residuals. Describe each of the plots in the
distribution of residuals. Indicate what this tells you about the Fisher conditions
necessary for the analysis of variance.
Turn in the JMP output that you have used to answer the questions.
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