1
THE UNIVERSITY OF WESTERN ONTARIO
LONDON
CANADA
Department of Psychology
Intersession
1.
Psychology 281
Third Exam
Medical researchers sometimes use a digital sonomicrometer to measure the blood vessel
diameters of cardiac patients before and after treatment. In one study, it is predicted that
the diameter of patients' blood vessels will decrease by more than 400 micrometers
following treatment with an experimental drug. To test this hypothesis, the blood vessel
diameters (measured in micrometers) of 8 cardiac patients are compared before and 1
week after administration of the drug, yielding the following data:
Patient IDs
019M
328M
114F
985M
167F
033F
664M
230F
Blood Vessel Diameters
Before Treatment
After Treatment
7850
6448
4023
8137
5775
5890
6704
7852
6015
4124
4157
6309
5775
4362
6832
5396
a) Perform whichever statistical procedure(s) is/are required to test the researchers'
hypothesis (α  .05). [10 points]
b) In addition to the average size of the blood vessels of cardiac patients, the variance of
their blood vessel diameters may also be significantly different from that of the general
(non-patient) population, which (in micrometers) is known to be 2,000,000. Perform the
appropriate statistical test(s) to see whether the variance of the 8 patients' beforetreatment blood vessels (from part 'a') differs significantly from the general population
value (α  .05). [8 points]
2.
Two new therapies designed to increase levels of self-esteem are tested in a clinical
population. Nine subjects are randomly assigned to a control group (C) which is exposed
to a placebo procedure. We also randomly assign 7 subjects to Therapy A (TA) and 9
other subjects to Therapy B (TB). Self esteem scores are measured for each group after a
2-month period and the following results are obtained (no subjects dropped out of the
experiment):
2
Group C:
Group TA:
Group TB:
X = 11.111
X = 14.429
X = 18.667
S = 2.848
S = 3.599
S = 2.872
a) Determine whether there is an overall significant treatment effect (α  .05). (12 points)
b) Assuming you found a significant treatment effect in part 'a' (even if you didn't),
perform post hoc analyses to determine which particular pairs of groups differ
significantly. Assign an alpha of .05 to each comparison that you make (10 points)
3.
A particular Intersession stats prof is noted for 2 things: the number of pages of notes his
students have to write down each night and the number of pieces of chalk he destroys
each night. To see if there is any relationship between these, a record is kept of the
number of pages of notes his students write during 6 different lectures in June and the
number of pieces of chalk the prof destroys on these nights. The following data were
obtained:
Night
# Note Pages
Monday
Tuesday
Wednesday
Monday
Tuesday
Wednesday
8
4
12
6
9
7
# Chalks Destroyed
5
1
7
4
8
2
a) Is there a significant positive correlation between # of note pages and # of pieces of
chalk destroyed (α  .05)? [10 points]
b) How many pieces of chalk would the prof be predicted to destroy on a night that his
students write down 10 pages of notes, and what are the 95% bounds to the error of this
prediction? [10 points]
4.
An educational psychologist is studying two different approaches to teaching 1st graders
basic concepts of arithmetic. She randomly assigns children to one of two different
groups which will be exposed to one or the other teaching-approaches and obtains the
children’s scores (out of 100) on an arithmetic test before and after 10 weeks of
instruction. She then tests to see whether there is a significant difference between the two
approaches in the amount by which the children’s scores change. Using the following
data, perform the appropriate analyses to address the educational psychologist’s research
question (α = .05).
Teaching Approach One
Teaching Approach Two
3
Scores Before
60
54
77
86
71
5.
Scores After
63
58
80
86
74
Scores Before
55
76
65
54
67
Scores After
75
79
80
54
87
According to genetic theory, when tall yellow begonias are crossed with short red
begonias they should produce 4 types of offspring in a 9:3:3:1 ratio, representing tall red,
tall yellow, short red, and short yellow flowers, respectively. A botanist tests the theory
by collecting the following data: the number of begonias of each type that resulted from a
tall yellow/short red crossing.
Tall red
Tall yellow
172
55
Short red
72
Short yellow
16
a) Do these data conform to the theory (α  .05)? [10 points]
b) The botanist has also created a non-toxic chemical fertilizer which she believes will
change the height and colour characteristics of begonias. She again crossbreeds tall
yellow begonias with short red begonias and sprays the offspring of these flowers daily
with the chemical fertilizer. She collects the following frequency data after spraying:
Tall red
Tall yellow
Short red
Short yellow
100
40
45
9
Based on the two data sets from parts 'a' and 'b', does it appear that the height and colour
characteristics of begonias can be significantly altered by the fertilizer (α  .05)? [12
points]
6.
The stress of taking an important exam has been suspected of influencing students'
quality of sleep. To test this hypothesis, we measure sleep quality (number of hours of
deep sleep per night) in a group of six undergraduates 1 month prior to an exam
(baseline), the night before an important exam (NB), and the night after the exam (NA).
We obtain the following information:
Baseline
Ti
21.0
ΣX2 = 227.22, and SSSubjects = 2.837
NB
NA
18.0
24.0
4
a) Is there a significant difference in sleep quality between the three measurement
periods (α  .01)? [12 points]
b) Prior to data collection it had been predicted that sleep quality at the baseline and NA
measurement periods would not differ significantly. Is this prediction supported by the
data, using α  .05? [6 points]
Answers
1. a) t = 2.061: reject Ho, the hypothesis/prediction is supported; b) χ2 = 6.675: do not reject Ho,
the variance does not differ significantly from 2,000,000
2. a) F = 13.61: reject Ho, a significant treatment effect exists; b) Q’s = 3.96, 3.10, and 7.06: all
reject Ho so all comparisons are significant
3. a) r = .829, t = 2.965: reject Ho, a significant positive correlation exists; b) 6.434 ± 5.453
4. (i) F = 39.26: reject Ho, the variances differ significantly so now do a Wilcoxon test; (ii) T =
22 (or 33): do not reject Ho, there is no evidence for any significant difference between the two
approaches
5. a) χ2 = 3,96: do not reject Ho, the theory is supported; b) χ2 = .905: do not reject Ho, the
fertilizer has no effect
6. a) F = 16.988: reject Ho, a significant difference exists; b) t = 2.914: reject Ho, the prediction
is not supported.