Statistics 402B & C
April 9, 2008
Exam
Name: __________________________
INSTRUCTIONS: Read the questions carefully and completely. Answer the questions
and show work in the space provided. Credit will not be given if work is not shown. Be
sure to answer all questions within the context of the problem. Refer to the computer
printout and graphs provided when appropriate. If the computer printout has the answer
use it, you do not have to do a hand calculation if it is already done for you by the
computer. Pace yourself. Do not spend too much time on any one problem. Point values
for each problem are given.
1. [32 pts] Name that design! For each of the following scenarios indicate what design
is used. Indicate the response variable, factors of interest, whether factorial crossing
is used to make treatments, nuisance factors and provide an ANOVA table listing all
sources of variation and associated degrees of freedom.
a. [8] A marketing firm sets up an experiment to see if coupons or mail-in rebates
have an effect on unit sales of a product. In each store, there is a display with the
product. The treatments are: (1) no coupon and no rebate, (2) $1 coupon and no
rebate, (3) no coupon and $1 rebate, (4) $1 coupon and $1 rebate. The marketing
firm selects 40 stores at random and randomly assigns 10 stores to each of the
treatment combinations.
b. [8] An experiment (field trial) is conducted to investigate the yield of soybeans
for 6 different seed companies. To get a better picture of yield across the state,
there are six locations that will be used in the experiment. At each location, the
test field will be divided in to six plots. Seed from each of the companies will be
assigned at random to one of the plots at each location so that all 6 seed
companies are used at each location.
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c. [8] A food company cuts and freezes French fries. The company wants to know
which of the five machines it uses to cut the French fries produces the most waste.
The cutting machines are in constant use. Different operators operate these
machines. The different operators have different skills and so can affect the
amount of waste produced. Each day a new load of potatoes is used and there
will be day-to-day variation in waste due to the size and shape of potatoes in a
days load. The company designs an experiment so that each of five operators
uses each machine once over a five-day period.
d. [8] An experiment is conducted to see the effect of fishing rod length and sinker
weight on the length of the cast. There are two fishing rod lengths: 6 feet and 7
feet. There are two sinker weights: 8 ounces and 12 ounces. Because casting
skill and strength may vary from one fisherperson to the next, 12 different people
will be used in the experiment. Each person will make one cast with each of the
four combinations of fishing rod length and sinker weight. The order of the four
casts will be randomized for each person.
2. [6] What is the primary advantage of using a block design over a completely
randomized design? In answering this question indicate when a block design should
be used.
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3. [32 pts] Bank examiners must complete a “work basket” of tasks in a satisfactory
fashion in order to become board certified. New “work baskets” are made for each
round of examinations and every effort is made to make them similar (in terms of
average score) from exam to exam. Two new “work baskets” (A and B) are being
evaluated. Three old “work baskets” (C, D and E) are included in the evaluation for
comparison. Five students will complete all of the “work baskets.” Five graders will
each grade five exams and assign a score out of 100. The evaluation is done as a
Latin Square design with the data presented below. Refer to the Analysis of Board
Certification Exams.
Student
1
2
3
4
5
1
D 68
A 68
C 73
E 74
B 80
2
A 65
E 77
B 85
C 76
D 71
Grader
3
E 76
B 84
D 72
A 57
C 76
4
C 74
D 65
E 68
B 79
A 59
5
B 76
C 75
A 62
D 64
E 68
a) [4] What are the response and conditions of interest?
b) [4] What are the two nuisance factors?
c) [6] Are there statistically significant differences among the “work baskets”?
Report the appropriate F-statistic, P-value, decision, reason for the decision and
conclusion.
d) [3] If q* = 3.18738, what is the value of Tukey’s HSD?
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e) [6] Below are the mean scores for the “work baskets”.
Work Basket
Mean
B
80.8
C
74.8
E
72.6
D
68.0
A
62.2
What can be said about the two new “work baskets,” A and B? Justify your
comments statistically.
f) [6] Suppose that you forget to include Grader in the analysis and so only had
student as the block. Construct an ANOVA table for that analysis using the
degrees of freedom and sums of squares from the computer output. You should
include sources of variation, degrees of freedom, sums of squares, mean squares
and any appropriate F-statistics.
g) [3] The F-statistic for the factor of interest is still statistically significant with the
analysis in f). Below is the display from Tukey’s HSD procedure for the analysis
in f).
Work Basket
Mean
B
A
80.8
C
A B
74.8
E
B
72.6
D
B C
68.0
A
C
62.2
Levels not connected by the same letter are significantly different.
What can be said about the two new “work baskets,” A and B?
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