STATISTICS 402 - Assignment 4
Due March 7, 2005
1. Oleoresin 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 (circular, diagonal or check and
rectangle) 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 are the response, conditions (factors and levels the experimenter is going to manipulate)
and units used in this experiment?
(b) The experimenter will use factorial crossing to create the treatment combinations. How many
treatment combinations will there be in the experiment?
(c) The experimenter would like to be able to detect a difference in treatment means of 2.5 standard
deviations while keeping both chances of error at 5%. How many units will the experimenter
need?
(d) With this number of units, what size difference in factor level means can be detected when
ALPHA=0.05 and BETA=0.10?
(e) Because of budget constraints, only 3 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.
(f) Come up with a randomization of the runs (assuming 3 units for each treatment combination)
for the experiment. That is, give me the randomized order that you would use if you were the
experimenter.
2. Most short-run supermarket strategies such as price reductions, media advertising, and in-store promotions and displays are designed to increase unit sales of particular products temporarily. Factorial
designs have been employed to evaluate the effectiveness of such strategies. Two factors examined are
Price Level (regular, reduced price and cost to the supermarket) and Display Level (normal display
space, normal display space plus end-of-aisle display, twice the normal display space). A complete
factorial experiment based on these two factors involves nine treatments. Suppose each treatment is
applied three times to a particular product at a particular supermarket. Each application lasts a full
week and the response variable of interest is unit sales for the week. To minimize treatment carryover
effects, each treatment is preceded and followed by a week in which the product is priced at its regular
price and is displayed in its normal manner. The data, numbers of items sold, are given below.
Price
--------------------Regular Reduced
Cost
Display
Normal
949
1045
1051
1321
1327
1222
1557
1536
1638
Normal Plus
1031
1163
1151
1801
1940
1956
2502
2558
2461
Twice Normal
1201
1178
1080
1546
1521
1448
1772
1803
1912
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(a) What is the response? What are the conditions? What are the units?
(b) Are there any differences among the nine treatments? Support your answer with a statistical test
of hypothesis.
(c) Are there any differences among the three different displays? Support your answer with a statistical test of hypothesis.
(d) If there are any differences among the three different displays, where are those differences? Support
you answer with a multiple comparison procedure.
(e) Are there any differences among the three different price levels? Support your answer with a
statistical test of hypothesis.
(f) If there are any differences among the three different price levels, where are those differences?
Support you answer with a multiple comparison procedure.
(g) Is there interaction between the two factors? Support your answer with a statistical test of
hypothesis.
(h) Construct an interaction plot. Comment on the plot and what it tells you about interaction
between the two factors.
(i) Construct a plot of residuals versus predicted values. Describe the plot and indicate what this
tells you about the conditions necessary for the analysis of variance.
(j) Look at the distribution of residuals. Describe the distribution of residuals. Indicate what this
tells you about the conditions necessary for the analysis of variance.
(k) What else does the distribution of residuals tell you about the experiment?
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