Statistics 402B & C
February 27, 2008
Exam 1
Name:___________________________
INSTRUCTIONS: Read the questions carefully and completely. Answer the questions and
show work in the space provided. This is the only work that I will look at. Partial 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 calculate by hand. Pace yourself. Do not spend too
much time on any one problem. Point values for each problem are given.
1. [12 pts] For each of the following statements indicate whether it is True or False.
a. True
False
A statistic is a value you compute from a sample.
b. True
False
An important reason why large samples are better than
small ones is that they tend to be more representative.
c. True
False
A major reason for having several measurements under the
same conditions is to be able to estimate the size of the bias.
d. True
False
Bias tends to go in different directions for different
measurements and to cancel when you compute averages.
e. True
False
The conditions of interest contribute to planned systematic
variation.
f.
False
An important reason why large samples are better than
small ones is that the larger the sample the smaller the
chance error.
True
2. [5 pts] A drug company does an experiment involving dosage level of a drug intended to
reduce stomach acid. There are two treatment groups with dosage levels of 150 mg and
75 mg, respectively. Also a control group that receives a placebo, a pill with 0 mg of the
drug, is included in the experiment. At the end of the experiment there are acid reduction
values for 8 individuals in the placebo group, for 11 individuals in the 75 mg group and
for 11 individuals in the 150 mg group. The drug company decides to select 3
individuals at random from the 75 mg group and 3 individuals at random from the 150
mg group to exclude from the analysis of the data so that there are an equal number of
individuals in each group. Is this random selection and exclusion a good idea? Explain
briefly.
1
3. [10 pts] A biology department is interested in comparing students’ understanding of the
frog’s anatomy based on their experiences with dissection. They decide to look at three
methods for presenting the material. One method will have students dissect a real frog,
another method will have students use a computer program that simulates the dissection
of a frog, and a third method will have students spend half the time with a real frog and
half the time with the computer program. The dissection (real, virtual or both) will be
conducted in the laboratory section associated with the biology class. There are hundreds
of these lab sections. The same amount of time will be spent on dissection regardless of
the dissection method (real, virtual or both). At the end of the unit, all the students’ will
take the same test on the anatomy of the frog. There are two different ways to conduct
the experiment. Experiment 1 – Select three lab sections at random and assign one
section, at random, to each of the methods. The individual students’ test scores in each
section will be analyzed. Experiment 2 – Select 15 lab sections at random and assign 5
sections, at random, to each of the methods. The average test score for each section will
be analyzed.
a. [4] What is the chance variation in the experiment? Describe in some detail the
source of this variation.
Experiment 1:
Experiment 2:
b. [6] Suppose the virtual dissection group had a statistically higher mean test score
compared to the other two groups. What generalization can be made?
Experiment 1:
Experiment 2:
2
4.
[8 pts] A laboratory has four different scales that could be used to obtain the mass of
objects. In order to see how accurate and precise each of the scales is a technician uses
each scale to repeatedly determine the mass of an object known to be 20 milligrams.
Below are histograms of the results of the repeated measurements. Describe the accuracy
(bias) and precision (variability) of each scale.
Scale 2
30
30
30
20
10
Frequency
40
Frequency
40
20
0
20
10
10
0
0
0
10
0
20
10
30
20
Weight
(g) (mg)
Weight
40
0
30
10
40
20
30
40
30
40
Weight (mg)
Scale 4
Scale 3
40
40
30
30
Frequency
Frequency
Frequency
Scale Scale
1
1
40
20
10
20
10
0
0
0
10
20
Weight (mg)
30
40
0
10
20
Weight (mg)
a. [2] Scale 1
b. [2] Scale 2
c. [2] Scale 3
d. [2] Scale 4
3
5. [12 pts] A psychologist does an experiment involving memory. One theory regarding
memory states that verbal material is remembered as a function of the degree to which it
was processed when it was initially presented. To test this theory an experiment is run
with literate adults. The first factor is learning group. Subjects in the Counting group
read through a list of words and count the number of letters in each word. Subjects in the
Rhyming group read a list of words and think of words that rhyme with each word on the
list. Subjects in the Adjective group read a list of words and think of adjectives that
modify the words, one adjective for each word. Subjects in the Imagery group read a list
of words and form vivid images for each word. None of these four groups is told that
they will later have to recall the words. Subjects in a fifth group, the Intentional group,
are asked to memorize a list of words for later recall. After subjects read through a list of
words three times, they are asked to write down all the words they can remember. The
number of words correctly recalled is noted for each subject.
a) [6] What are the response, conditions and experimental units?

Response

Conditions

Experimental units
b) [3] Give an outside variable that should be controlled in this experiment. Explain
briefly how it can be controlled.
c) [3] Explain briefly how replication will be included in this experiment.
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6. [28 pts] The experiment described in 5 is performed using 100 adults of all ages. There
are 20 adults randomly assigned to each memory group. Refer to the JMP output for
Memory Experiment.
a) [2] With Alpha = 0.05 and Beta = 0.10, what size difference learning group means
will this experiment be able to detect?
b) [4]
Test
the
hypothesis
that
the
treatment
effects
are
zero
against the alternative that at least one is not
zero. Be sure to report the appropriate test statistic, P-value, decision, reason for the
decision and a conclusion within the context of the problem.
H 0 :  1   2   3   4   5  0
c) [5] Estimate the size of the five learning group effects.
d) [6] From the computer output what is the value of Kramer-Tukey’s HSD? Using the
HSD which differences in sample mean number of words recalled for the five
learning groups are statistically significant.
5
e) [4] The value of t* for computing the LSD is 1.98525. What is the value of the LSD?
How will the results of the comparisons using the LSD analysis differ form the
results of the comparisons using the HSD?
f) [3] Comment on the plot of residuals versus learning group and the sample standard
deviations for the Learning groups. What do these tell you about the Fisher
conditions necessary for the analysis of variance?
g) [4] Comment on each plot in the distribution of residuals. What does this tell you
about the Fisher conditions necessary for the analysis of variance?
6