Study Guide for the Mid-Term Exam

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```					Statistics 490:01                                                                                                Spring 2005

Introduction to Experimental Design
Study Guide for the Mid-Term Exam

The mid-term exam will be given on Thursday 03/24 during our usual class time, though only for about 2 hours. The
general coverage is most of Chapters 1-5 and Sections 14-1 and 14-2, excluding any omitted sections (i.e., those not
explicitly covered in class). You will be permitted to use up to three pages of handwritten help-sheets (front and back,
8.5  11), but you may not use the textbook. Copies of all needed statistical tables will be provided with the exam
itself. You will need a calculator, but you must show all intermediate results, as an answer alone will earn no credit.

Preparing for the exam should begin with a thorough review of all of the assignments (there have been 5 so far).
Solutions to all of the assignments are (or will soon be) available on our class website. Some sample exam problems
appear below so that you may acclimate yourself with the format of the exam. There will be two parts to the exam:
conceptual and applied. The conceptual part will be generally non-computational and require you to provide a detailed
explanation to some problem. The applied part will consist of problems that require the proper implementation of a
testing procedure (e.g., ANOVA, multiple comparisons, contrasts). Examples of both types of problems appear below.

1. A medical researcher suspects that giving post-surgical patients large doses of vitamin E will speed their recovery
time by helping their incisions heal more quickly. Design an experiment to test this conjecture. Be sure to identify
the factors, levels/treatments, response variable, and the role of randomization.

2. Three groups of students are to be tested for the percentage of high-level questions asked by each group. As
questions can be on various types of material, six lessons are taught to each group and a record is made of the
percentage of high-level questions asked by each group on all six lessons. Show a hypothetical data layout for this
experiment and outline its ANOVA table with the proper entries for degrees of freedom.

3. What is the main advantage of a randomized block design over a completely randomized design? Under what
conditions would the completely randomized design have been better?

4. Explain why the treatment combinations in factorial experiments should be replicated at least twice.

5. To see how much of a difference time of day made on the speed at which he could download files, a college
sophomore performed an experiment. He placed a file on a remote server and then proceeded to download it at three
different time periods of the day. He downloaded the file 48 times in all, 16 times in each time period. The data
appears below, where the response variable is the time (in seconds) to fully download the file.
7:00AM            5:00PM          12:00AM
68               299             216
138               367             175
75               331             274
186               257             171
68               260             187
217               269             213
93               252             221
90               300             139
71               296             226
154               204             128
166               190             236
130               240             128
72               350             217
81               256             196
76               282             201
129               320             161
(a) Determine whether time of day has an effect on the download time. Use level of significance  = 0.05.
(b) If appropriate, use the SNK multiple comparison procedure to test for pairwise differences between the three
treatment means. Use level of significance  = 0.05.
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6. To determine whether there is a difference in leakage between the capacitors of three vendors (A, B, and C), six
samples were randomly drawn from each vendor and the following leakage readings (in milliamperes) were
recorded.
Vendor A                     Vendor B                               Vendor C
7.3                         10.7                                   10.5
8.0                         10.2                                   10.1
8.1                         10.2                                   10.8
8.5                         10.7                                   11.6
8.4                          9.9                                   11.4
7.5                         11.0                                   10.8
(a) Determine whether there is a significance difference in average leakage among the three vendors. Use level
of significance  = 0.05.
(b) After examining the residual plot and Normal Q-Q plot of the residuals below, comment on model

Residual Plot                                                                  Normal Q-Q Plot
0.5

0.5
Sample Quantiles
Residual

0.0

0.0
-0.5

-0.5

8.0   8.5     9.0     9.5        10.0     10.5                                 -2        -1            0              1   2

Predicted Value                                                                Theoretical Quantiles

(c) If vendor A is the present supplier and vendors B and C are competitors, construct a set of two meaningful
orthogonal contrasts, test them, and discuss the results.

7. A nutritionist wishes to compare three well-known dietary products. Using data on girth (i.e., a function of height
and weight), age, and metabolism, she matches 18 of her male clients into six groups of three each and randomly
assigns one member of each group to one of the three dietary treatments. The following data represent the amount of
weight lost (in pounds) lost by the 18 clients after six weeks of treatment.
Group                       Diet 1                                 Diet 2                  Diet 3
1                          10.4                                   12.1                     9.0
2                           9.8                                   14.5                     9.6
3                           7.3                                   10.0                     9.8
4                           7.5                                    9.9                    10.7
5                           8.6                                   14.2                    11.1
6                          10.7                                   10.5                    10.5
(a) Identify the type of design the nutritionist has employed.
(b) Determine whether there is a significant difference in average weight loss between the three diet types. Use
level of significance  = 0.05.
(c) If appropriate, apply Fisher’s LSD multiple comparison procedure to test for pairwise differences between
the three diet means. Use level of significance  = 0.05.
(d) If the goal is to lose as much weight as possible, use your above results to make a recommendation.

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8. The adhesive force of a certain glue was determined under three fixed humidity and three fixed temperature
conditions. Four readings were made under each set of conditions. The experiment was completely randomized,
yielding the following partial ANOVA table.
Source                  df           SS                    MS                 EMS          F
H                                   9.07
T                                   8.66
HT                                 6.07
Error
Total                               52.30

(a) Complete the ANOVA table and carry out all relevant tests. Use level of significance  = 0.05.
(b) State the mathematical model for this experiment with each term explicitly defined.

9. A physical education experiment will be conducted to investigate the effects on heart rate of four types of exercise.
Five subjects are chosen at random from a physical education class. A subject does each exercise twice. The 40
measurements are done in a completely randomized order, and each subject is allowed 10 minutes rest between
exercises.
(a) Show a hypothetical data layout for this experiment and outline its ANOVA table with the proper entries for
degrees of freedom and expected mean squares (EMS).
(b) Explain how to perform the relevant F-tests.

10. An experiment was designed to study the effect of two factors on the amplification of a stereo recording. The factors
were type of amplifier (four brands) and type of receiver (two brands). For each combination of factor levels, three
tests were performed in which decibel output was measured. A higher decibel output means a better result. The
coded results appear below.
Amplifier Brand
A      B        C         D
9      8       8         10
R1              4     11       7         15
12     16       1          9
7      5       0          6
R2              1      9       1          7
4      6       7          5
(a) Carefully analyze this data, assuming that both factors are random. Use level of significance  = 0.05.
(b) Plot both interaction plots.
(c) Based on your above results, which receiver and/or amplifier brand should be used to maximize decibel
output?

11. Porosity readings on condenser paper were recorded for paper from four rolls taken at random from each of three
lots. The data appears below.
Lot                       Lot I                                          Lot II                                Lot III
Roll       1         2             3          4          1          2              3     4           1     2          3     4
1.5       1.5           2.7        3.0        1.9        2.3            1.8   1.9         2.5   3.2        1.4   7.8
Obs.      1.7       1.6           1.9        2.4        1.5        2.4            2.9   3.5         2.9   5.5        1.5   5.2
1.6       1.7           2.0        2.6        2.1        2.4            4.7   2.8         3.3   7.1        3.4   5.0
(a) Identify the type of design the researcher has employed.
(b) Carefully analyze this data, assuming that lots are fixed and rolls are random. Use level of significance
 = 0.05.
(c) How would your results change (if at all) in part (b) if lots were random as well?

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