Download Psychology 281 – Final Review Questions

Psychology 281 – Final Review Questions
1. In the general population, the Life Stress Scale has a mean of 143.5 and a standard deviation
of 23.6. Medical researchers hypothesize that people with high blood pressure are exposed to
more Life Stresses than is the general population. To test this hypothesis, they selected 42
patients with high blood pressure and administered the Life Stress Scale.
a) The mean Life Stress score for the high blood pressure sample was 152.6. Can the
researchers conclude with  .03 that their hypothesis is correct?
b) On the, basis of a second study, the researchers determined that the 94% confidence interval
for the mean Life Stress score of high blood pressure people was 144.125 to 156.675. How many
subjects were used in this second study?
2. Six students were given a test at the beginning of the school year and again, 3 months later.
The purpose of the testing was to assess the extent to which their scores improved as a result of
the course work they had done during the 3 months. Their scores on the two tests (each out of
100) are as follows:
First Test
Second Test
72
78
82
80
65
68
74
75
69
68
66
74
(a) Perform the appropriate statistical test to see if students' scores improved significantly from
the first to the second test ( .10).
(b) The same students now underwent a 4-week intensive program of instruction and were then
given a third test (also out of 100). Their scores on this test were:
Student:
1
2
3
4
5
6
Third Test:
85
87
76
76
77
82
Is there an overall significant difference in the students' performance on the three tests (  .05)?
3. A western separatist organization claims that Ontario is wealthier because students are better
trained and consequently are wore competitive in the job market. An educational psychologist
tests this notion by comparing standardized aptitude test scores (LSAT) of Ontario and
Saskatchewan university students. The scores of several randomly selected Ontario and
Saskatchewan students are listed below:
Ontario Sample
Saskatchewan Sample
42.7
33.5
39.3
38.6
30.5
26.2
36.6
27.7
38.3
46.0
40.5
32.3
44.6
34.5
42.4
27.0
42.6
28.9
X-bar = 39.722
X-bar = 32.744
s2 = 18.214
s2= 41.238
Test the western separatist organization's hypothesis ( .05).
4. Experience has shown that 50 percent of the time, a particular union-management contract
negotiation had led to a contract settlement within a 2-week period, 60 percent of the time the
union strike fund has been adequate to support a strike, and 30 percent of the time both
conditions have been satisfied. What is the probability of a contract settlement given that you
know that the union strike fund is adequate to support a strike? Is settlement of a contract within
a 2-week period dependent on whether the union strike fund is adequate to support a strike?
5. To determine whether the location of a brain injury in the left hemisphere was related to
language dysfunction, researchers measured language production ability in 90 patients. The
number of patients scoring above average and below average on the test is presented in the
following table as a function of the location of the injury.
Injury Location
Left Anterior
Score
Below
Above
16
6
Left Temporal
15
18
Left Parietal
17
18
a) Do these results warrant the conclusion that classification as above or below average on the
test of verbal production is related to location of injury? ( .05)
b) In the general population) the anterior, temporal, and parietal areas account for 40%, 23% and
37% of the relevant area of the brain. Do the results in the preceding table permit the researchers
to conclude that the probability of an injury in the different locations depends on more than
simply the size of the different brain areas? ( .05)
6. According to legend, the beaches in the fantasy kingdom of Loof Lirpa are lined with
precious stones, specifically, diamonds, rubies and sapphires. While on vacation there you
combed the beaches and found 6 diamonds, 7 rubies and 3 sapphires. Unfortunately, getting
them out of the country is another story. When you arrive at the airport you find your cab fare is
6 precious stones. How many ways to pay it are there if:
a) your payment must include at least two diamonds?
b) you decide to pay with three diamonds, two rubies and one sapphire?
You now have 3 diamonds, 5 rubies and 2 sapphires. Unfortunately, the guy who collects the
airplane boarding tax also demands a precious stone in payment and randomly selects one from
your bag. If this man receives a diamond, he will let you board the plane immediately, however,
if he receives anything else there is a 50:50 chance he'll send you to the emigration desk.
c) What is the probability that he allows you to board the plane?
d) Given that he allowed you to board the plane, what is the probability that he selected a
diamond from your bag?
7. A box contains 5 red chips and 3 blue chips. You are to draw a chip at random, without
replacement, until the first blue chip is drawn. Let the random variable X denote the number of
draws.
a) Find the probability distribution of X.
b) Find the mean of this distribution.
c) Find the variance of this distribution.
8. Of the customers who do business at a rental car agency, 20% prefer large automobiles.
a) In a randomly selected group of 15 customers what is the probability that at least 3 of the
customers prefer large automobiles?
b) In a randomly selected group of 100 customers what is the probability that between 16 and
26 (inclusive) of the customers prefer large automobiles?
c) What is the minimal number of large automobiles the agency should have on hand to ensure,
with a probability of at least 0.9, that it can meet the large automobile demand of a randomly
selected group of 225 customers?
9. An experimenter is interested in determining the effects of shock on the time required to
solve a set of difficult problems. Subjects are randomly assigned to four experimental conditions.
Subjects in Group 1 receive no shock; Group 2, very low-intensity shock; Group 3, mediumintensity shock; and Group 4, high-intensity shock. There are 12 subjects assigned to each
condition. The means for the different groups are 9.25, 7.33, 13.0, and 16.25 for Groups 1, 2, 3,
and 4, respectively. Further, when each raw score is squared and these squared values are added
together the sum is 7434. Is there a significant ( .05) difference among the four groups? If
possible, do post-hoc pair-wise comparisons (Newman-Keul) at  .05.
10. It is known that the mean number of errors made on a particular pursuit rotor task is 60.9. A
physiologist wishes to know if persons that have had spinal cord injury, but who are now
"apparently" recovered, perform less well on this task. In order to test this, a random sample of 8
persons that had spinal cord injuries is taken and administered the pursuit rotor task. The number
of errors made by each subject is shown below.
63, 66, 65, 62, 60, 68, 66, 64
a) Is there evidence to believe that "recovered" patients are impaired in performing the task? (
.01)
b) Form the 90% confidence interval for the mean.
11. The Acme company produces flashlight batteries that have a true mean lifetime of 21.4
months and a standard deviation of 1.2 months. The Apex company produces flashlight batteries
with a true mean lifetime of 25.5 months and a standard deviation of 1.8 months. A random
sample of 50 flashlight batteries from Apex is taken and a random sample of 70 batteries from
Acme is taken. What is the probability that the difference between the mean lifetimes of these
two samples will exceed 4.5 months?
12. A random numbers table of 250 digits showed the following distribution of the digits 0, 1,
2,...,9. Does the observed distribution differ significantly from the expected distribution? ( 
.05)
Digit:
Observed frequency:
0
17
1
31
2
29
3
18
4
5
6
7
14
20
35
30
8
20
9
36
13. A drug company has developed a new analgesic drug (for pain relief) which seems to be very
potent at very low doses. This drug is tested at two different doses along with a placebo on
separate groups of subjects. The subjects' pain thresholds are measured by recording reaction
time to a mildly painful stimulus. The deviations from the mean reaction time for each group
are given in the table below:
Placebo
-1.2
2.3
1.6
-2.1
-1.8
2.0
-0.8
1 mg
10 mg
0.5
1.6
-2.1
2.4
-1.7
-0.9
1.3
-0.8
-0.3
1.1
-2.0
0.7
-1.6
2.2
0.2
1.0
-1.6
The mean reaction times for the three groups were 18.1 sec, 22.0 sec., and 29.8 sec respectively.
a) Is there a significant analgesic effect of the drug treatment? (Use   .01)
b) Do Newman-Keul's multiple comparisons to determine which groups differ significantly.
(Use  .05)
14. There was once a man who had two sons he loved equally. The man wished for both sons to
become doctors, but he knew that the first son was not as bright as the second. In the first term of
medical school the first son only passed 45% of the tests, while the second son passed 80% of
the tests. The father then determined that he could not support both sons in the second term of
medical school, but because he loved them equally he randomly selected one to continue.
Assuming that the sons would perform at the same level they showed in the first term, answer the
following:
a) What is the probability that the chosen son failed the first test of the second term?
b) If we know that the son passed the first test of the second term, what is the probability that
this was the first (less bright) son?
15. A large car rental agency sells its cars after using them for a year. Among the records for
each car are mileage and maintenance costs for the year. To evaluate the performance of a
particular car model in terms of maintenance costs, the agency wants to use a 95% confidence
interval to estimate the increase in costs for each additional 1000 miles driven. Use the following
data to accomplish this objective:
Car
Miles Driven (in 1000s)
Costs
1
2
3
4
5
6
54
27
29
32
28
36
326
159
202
200
181
217
16. When mice are subjected to stress their endogenous opioid system is activated and the mice
increase food consumption in the post-stress period. To test if a loud noise (85 db) is a stressful
stimulus, we expose 10 mice to the loud noise for 1 hour and expose 8 mice to normal room
noise levels. We measure their food consumption over the next two hours and obtain the
following data:
Loud noise
Normal noise
1.05
0.80
1.15
0.25
1.60
0.30
0.95
1.85
0.55
1.00
0.60
0.80
0.75
0.65
0.70
0.60
0.55
0.85
Do these data suggest that the loud noise activated the opioid system and increased food
consumption? (  .05)
17. The provincial government is currently investigating the issue of underfunding in
universities. They have data which indicate that North American universities spend $10,000 on
each student, on average, with a standard deviation of $1500. They also have data. indicating that
student personal income averages $9,000 per year, with a standard deviation of $3000. (Both
expenses to universities and incomes of students are normally distributed.) They decide to survey
8 Ontario universities and 1000 students. Government funding will only be raised if the average
student income is below $8,900 and average university expenses are above $10,100. What is the
probability of this event?
18. Is there a significant difference between the Psychology 281 grades earned by students from
different faculties? To address this question, the Psychology 281 final exam scores of a random
sample of 40 Social Science students were compared to those of 50 Science students. The means
and variances of these scores are as follows:
Social Science
n = 40
Science
n = 50
X-bar = 70.5
X-bar = 72.1
s2 = 200
s2 = 250
a) Determine whether a significant difference exists between the mean scores of these samples
(  .05).
b) Suppose that, in fact, the mean final exam scores of the populations of Social Science and
Science students differ by 3 points. Given this, what is the probability that you would fail to
detect a significant difference based on the sample sizes and variances used in part 'a' (still using
  .05)?
19. Certain dosages of a new drug developed to reduce a smoker's reliance on tobacco may
reduce one's pulse rate to dangerously low levels. To investigate the drug's effect on pulse rate,
different dosages of the drugs were administered to 6 randomly selected patients, and 30 minutes
later the decrease in pulse rate was recorded.
Patient
1
2
3
4
5
6
Dosage
2.0
1.5
3.0
2.5
4.0
3.0
Decrease in pulse rate
15
9
18
16
23
20
a) Is there evidence of a linear association between drug dosage and change in pulse rate at the
.10 level?
b) What is the predicted decrease in pulse rate for a person receiving a dosage of 3.5, and what
are the 99% bounds to the error of this prediction?
20. Santa keeps a record of the weights of packages he loads on his sled. In past years, the
weights of the packages have been normally distributed with a mean of 9.0 kg and a variance of
6.25.
a) Santa wants to make sure Rudolf and the team can pull the sled. If Rudolf and the team can
only pull the sled if the total package load does not exceed 2000 kg and Santa puts a random
sample of 233 packages on the sled, what is the probability that Rudolf and the team won't be
able to pull it?
b) This year Santa suspects that the packages are lighter than usual. A random sample of 20
packages has a mean weight of 8.5 kg. Are his suspicions correct? (  .05)
c) Assume that Santa doesn't know what his mean package weight over the years has been. On
the basis of this year's information, create a 99% confidence interval for the true mean package
weight.
21. Nausea is a common symptom among postoperative patients. A group of physicians are
interested in comparing two new drugs, A and B, for their effectiveness in preventing
postoperative nausea. One hundred and eighty patients scheduled for surgery were used in the
study, with 60 assigned to receive each drug or a placebo. After surgery, each patient was
classified according to the degree of nausea he reported. The results are as follows: do they
indicate a difference between the drugs and the placebo in terms of their effect on nausea? ( 
.05)
DEGREE OF NAUSEA
Drug A
Drug B
Placebo
None
Slight
Moderate
High
40
36
30
10
12
16
6
4
8
4
8
6
22. The mean IQ of all female students at UWO is 112 with a variance of 64. The mean height of
all male students at UWO is 68 inches with a standard deviation of 3.4 inches.
a) What is the probability that a female student chosen at random at UWO has an IQ between
107 and 116?
b) What is the probability that a male student chosen at random from UWO will be shorter than
64 or taller than 70 inches?
c) If you observe a couple on a date (assume there is a female and a male), both of whom are
UWO students, what is the probability that the woman has an IQ of greater than 100 and the man
is shorter than 74 inches?
23. Because of the acid rain problem, there is a small lake in northern Ontario which has only 8
fish left: 4 trout and 4 pike. Suppose you decide to go fishing in the lake one day and plan to stop
as soon as you catch the first trout.
a) Create the probability distribution for the total number of fish you will return with assuming
you keep all the fish you catch.
b) Below is the probability distribution for the number of fish caught if you decide to stay out
until you catch 2 trout. What are the mean and variance of this distribution?
x
p(x)
2
3
4
5
6
.2143
.2857
.2572
.1714
.0714
24. Researchers wanted to determine the kinds of people who visited the London Art Gallery.
They asked 400 visitors their residence (London, Other Ontario, or Not Ontario) and their ages,
which were classified as young (Y: m ore than 1 standard deviation below the mean), somewhat
young (SY: between -l standard deviations and the mean), somewhat old (SO : between the mean
and +1 standard deviations), and old (0: more than 1 standard deviation above the mean). The
results are presented in the following table.
Y
London
8
Other Ontario 12
Not Ontario 20
Age
SY
SO
O
46
43
41
65
48
37
41
27
12
a) Is there a significant relationship between the residence of people and their ages, with 
.10?
b) Does the London Art Gallery attract more people from one of the three residence areas than
from another, ignoring age?(   .05)
c) Does it appear that the distribution of the ages of visitors from London fits a normal
distribution? (  .05)
25. One of the ways of assessing the quality of a university is in terms of the amount of research
funds the faculty bring to the university. An administrator at Warthog University knows that,
historically, Warthog professors have brought in an average of $5870 per person in research
funds, with a standard deviation of 550. She also knows that professors at arch-rival Bison
University have attracted an average of $3925 per person, with a variance of 245025. Concerned
that Bison may be catching up to Warthog, the administrator takes a sample of 44 Warthog
professors and 39 Bison professors and records their grant amounts for the most recent year.
a) Assuming that the means and variances have not changed, what is the probability that in these
samples the Warthog mean exceeds the Bison mean by at least $2000?
b) The administrator suspects that the difference between Warthog and Bison professors has
narrowed because of recent hiring at Bison. If, in fact, the true difference is now $1550, what is
the probability that the administrator detects that the difference is narrowing when she samples
50 faculty from each university? ( = .05)
26. Simple reaction times to green, red and yellow instrument panel lights were compared. The
three light colours were randomly assigned to 31 different subjects who were instructed to press
a button in response to the light. The data below are average reaction times (in milliseconds) for
the 31 subjects.
a) Is there an overall difference among the light conditions? ( = .01)
Green
Red
Yellow
mean
201
215
218
variance
2.9
3.5
3.4
ni
10
11
10
b) Due to the fact that “green” means “go” when driving, prior to running this experiment, the
researchers expected that green lights would be responded to faster than red lights. Is this
expectation borne out by the results? ( = .05)
27. Rawlings, one of the companies that makes baseball uniforms, has noticed that 45% of their
customers request blue lettering, 35% request red lettering and 20% request some other colour.
Among those requesting blue lettering, 60% also request player numbers on the sleeves while
only 40% of the other customers do.
a) What is the probability that the next order Rawlings receives will not be one requesting player
numbers on the sleeves?
b) If the next order does request player numbers on the sleeves, what is the probability that it is
an order for red lettering?
c) In the past year, there have been exactly 50 orders. Twenty have been for blue lettering (14
with numbers on the sleeves), 15 have been for red lettering (8 with numbers on the sleeves) and
15 have been for green lettering (5 with numbers on the sleeves). If Rawlings randomly selects
10 of these uniforms to put into their brochure, what is the probability that they select no more
than 1 green uniform?
d) If they did get exactly 1 green uniform, what is the probability that it had player numbers on
the sleeve?
28. Wilson is a manufacturer of golf balls. Through the years, they have attempted to make a
ball that when hit by the average golf professional will travel an average of 280 yards with a
standard deviation of 20. (We can assume that the distribution is normal.) In addition, they have
discovered that their ball tends to go farther than the ball of their main competitor, Spalding.
That is, when the same person hits balls from both companies, the Wilson ball goes farther 60%
of the time.
More recently, Wilson has been worried about the quality of their balls and decides to subject
them to the following test. Sixteen times an average golf professional hit a Wilson ball and a
Spalding ball, producing the following results (in terms of yards the balls travelled).
Hit
Wilson
Spalding
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
297
277
275
250
300
296
270
282
304
293
265
264
280
272
266
279
284
286
280
255
288
294
290
289
270
288
278
299
286
255
283
275
a) Does it appear that the variance for the Wilson ball has changed? ( = .05)
b) Construct a 98% confidence interval for the proportion of times the Wilson ball goes farther
than the Spalding ball.
29. "Twenty One" and "Who wants to be a millionaire" are popular TV game shows where
knowledgeable contestants can make big money very quickly. Because there is theoretically no
limit to the amount a contestant could win on "Twenty One", its promoters claim that it is the
most lucrative show on TV. To see if this is true, you record the amount won by 16 randomly
selected recent contestants, 8 of whom appeared on "Twenty One" and 8 others who appeared on
"Millionaire". Use these data to see whether contestants are in fact likely to win more money, on
average, on "Twenty One" than on "Millionaire." ( = .05)
Dollars Won
"Twenty One"
"Millionaire"
1,765,000
25,000
105,000
55,000
1,000
1,000,000
125,000
250,000
1,000
125,000
64,000
64,000
250,000
32,000
25,000
1,000
30. A psychologist was studying the effectiveness of several treatments to help people quit
smoking. In one treatment, smokers heard a lecture about the effects of cigarette smoke on the
human body, accompanied by graphic slides of those effects. In the other treatment, smokers had
daily phone conversations with a therapist who encouraged them not to smoke that day. To
control for effects of age and sex, the psychologist assigned people to the experimental groups in
pairs matched on those variables. The data, in the form of number of hours without a cigarette are
as follows:
Pair
1
2
3
4
5
6
7
8
Lecture + Slides
Daily Encouragement
105
98
121
99
65
130
108
57
122
86
127
92
85
152
92
63
a) Do the treatments lead to different lengths of time before subjects start smoking again? ( =
.05)
b) Form the 99% confidence interval for the true difference between the two treatments.
31. Scores on many tests of mental ability are normally distributed in the population. To see
whether scores on a particular test are also normally distributed among University students you
administer the test to 250 male students and to 250 female students and record the number of
students in each sample who score within different intervals. These data are summarized below,
where the intervals are expressed in z-score or standard deviation units:
Interval
< -2.0 s
-2.0 to -1.0 s
-1.0 to 0.0 s
0.0 to +1.0 s
+1.0 to +2.0 s
> +2.0 s
# males
7
36
80
86
30
11
# females
10
32
85
88
20
15
a) Does the distribution of the male students' scores differ significantly from a normal
distribution? ( = .05)
b) Is there a significant difference between the male and female distributions? ( = .01)
32. Six racing snails are arguing about how to increase their crawling speed. One of them claims
that she can move faster if she stretches as far as possible with each slither. A second claims that
snail speed is increased if a snail takes smaller but faster slithers. And a third snail argues that
speed can only be increased if a racing snail actually leaps forward between slithers. The snails
agree that they will race three times, trying each of these approaches. Their 1 meter race times, in
minutes, are as follows:
Snail
Stretch
Small Slithers
Sam
Susan
Sarah
Simon
Sadie
Sanford
10
8
7
9
8
9
9
9
8
Leap
11
12
13
11
12
13
11
14
15
a) Is there an overall significant difference between mean race times using the three different
techniques? ( = .05)
b) Regardless of your results in part ‘a’, determine which crawling methods differ from each
other. ( = .05)
33. Psychologists interested in human intelligence have studied the relationship between people's
performance on IQ tests and the speed with which they can encode visual stimuli. It is believed
that faster encoding speed may contribute to higher IQ scores. The following are the encoding
speeds [ES] (in milliseconds) and IQ scores of 8 adult subjects.
Subject
ES
IQ
1
2
3
4
5
6
7
8
111
88
125
76
108
110
95
85
103
119
90
127
98
82
108
115
a) Use these data to see whether a significant negative relationship exists: i.e., whether faster, or
shorter, encoding speeds are associated with higher IQs. ( = .05)
b) Use the data to generate a 95% prediction interval for the IQ score of an adult with an
encoding speed of 100 milliseconds.
34. At the Frog Olympics, all the events involve jumping and croaking. Traditionally, in the
first event, frog athletes jump for distance, then croak for volume, then jump for distance again.
The President of the Interpond Frog Olympics Commission believes that the croaking takes a lot
out of the athletes, and that their average jumping distance after croaking is shorter than their
average jumping distance before croaking. He orders an assistant to collect data on a sample of
frogs. The following are the distances (in cm.) recorded before and after croaking:
Frog
Distance Before Croaking
1
2
3
4
5
6
7
8
Distance After Croaking
82
69
75
48
99
61
55
92
79
72
65
44
91
52
48
80
a) Do frogs jump further before croaking than after? ( = .05)
b) Form the 99% confidence interval for the difference between before-croaking and aftercroaking jumping distances.
35. In a recent (2002) article, researchers investigated whether there was any relationship
between the personality trait of sensation-seeking and involvement in the game of chess.
Reported below are data from 8 University students who completed a measure of sensationseeking (range of possible scores: 0-100, high scores = high sensation-seeking) and reported
how often (games/week) they played chess:
Sensation-Seeking
46
83
17
75
37
8
62
24
Chess games
6
4
0
8
3
1
4
4
a) Use these data to see whether there is a significant correlation between sensation-seeking and
frequency of chess-playing. ( = .05)
b) If a student scored 50 on the sensation-seeking scale, how often would you predict he or she
would play chess, with 99% confidence?
c) Among expert chess players, the slope for predicting frequency of chess-playing from
sensation seeking is .575. Is the slope in the sample of 8 University students significantly
different from this? ( = .05)
36. Females’ reaction times (RTs) on a particular test of perceptual speed are normally
distributed with a mean of 750 ms. and a standard deviation of 150. The RTs of males on this
test are also normally distributed, with a mean of 900 ms. and a standard deviation of 175.
a) 50 females and 50 males are randomly selected and given the test of perceptual speed. What
is the probability that the mean RT of these 50 males will be more than 225 ms. slower (i.e.,
higher) than the mean of the 50 females?
b) It is hypothesized that males who practice regularly on tests of perceptual speed may be able
to lower their RTs (i.e., become faster). 40 randomly selected males spend 20 minutes each day
for 2 weeks practicing on tests of perceptual speed, at the end of which their mean perceptual
speed RT is recorded. If, in fact, this amount of practice would reduce males’ RTs to 800 ms.,
on average, what is the probability that you would be able to draw the correct conclusion based
on the data from the sample of 40 males (using  = .05)?
37. Three stats professors are riding in a car, heading for a pub after giving a final exam. The car
is hit by a falling meteor. Meanwhile, across town, the manager of a restaurant chain wants to
know how much a typical customer spends on dinner. She randomly samples 49 credit card
receipts from recent evenings, recording the pre-tax amount on each receipt. The sum of all 49
amounts is $1354.85. The sum of the squared amounts is 43185.43.
a) Find the 96% confidence interval for the true mean pre-tax amount on dinner receipts at this
restaurant chain.
b) At the end of the year, the manager learns that the average customer spent $28.15 on dinner.
In the new year, she runs a promotion intended to get customers to spend more money. One
week into the campaign, she randomly samples 8 receipts, recording the pre-tax amount, to test
the campaign’s effectiveness. She records the following amounts (in dollars):
26.25
29.49
30.35
32.80
28.66
33.60
29.70
32.15
What conclusion should she reach about the effectiveness of the campaign? ( = .05)
38. A sample of 200 people were given a test designed to measure how extraverted they are.
These people were classified as either high, moderate, or low in extraversion on the basis of their
responses to the test. The following shows the number of people who fell into each category:
Extraversion Categories
High
75
Moderate
Low
68
57
a) Are people high, moderate, or low in extraversion equally represented in the population from
which this sample of 200 was drawn? ( = .05)
b) The same 200 people were also classified as high or low in problem-solving ability on the
basis of their performance on a nonverbal problem-solving task. The following shows how
many people fell into each category:
Extraversion Categories
High
High
Moderate
Low
36
48
34
39
20
23
Problem-Solving
Low
Is there a significant relationship between degree of extraversion and problem-solving ability?
( = .01) (6 marks)
39. A researcher wants to know whether dogs and cats differ in intelligence, and whether the
difference varies with the amount of training they receive. She develops a set of non-verbal
intelligence tests involving memory and processing time, and administers these to each type of
animal. Some of the animals receive training on the relevant tasks for one month. A second
group of animals receives two months of training before being tested, while a third group gets no
training. N = 10 for each group. Mean scores on the intelligence test for samples of dogs and
cats are given below:
Training period
Dogs
Cats
0 months
1 month
2 months
 = 25.9
 = 28.7
 = 39.6
s2 = 3.5
s2 = 4.1
s2 = 6.3
 = 22.1
 = 23.4
 = 25.7
s2 = 2.9
s2 = 4.4
s2 = 5.8
a) Do the appropriate analysis to answer the researcher’s questions. (all  = .05)
bb) Regardless of your answer in part a., carry out tests to determine which training periods
differ in their effects on intelligence. ( = .01)
40. A researcher believes that people who believe in paranormal phenomena will obtain higher
scores on the personality dimension of openness-to-experience. To test this belief, the
researcher takes 8 randomly-selected people and gives them 2 tests: one is a 50-item test that
measures the extent to which they endorse beliefs in paranormal phenomena and the other is a
30-item test that measures their openness-to-experience. The following data were obtained:
Subjects
Paranormal beliefs
Openness-to-experience
1
2
3
4
5
6
7
8
40
20
48
6
30
26
42
12
22
14
24
9
23
20
27
7
a) Do these data provide significant support for the researcher’s belief ( = .05)?
b) Use the data to generate a 95% prediction interval for the openness-to-experience score of a
person with a paranormal beliefs score of 25.
41. Contestants in a new game show on television move down a corridor which has 3 doors on
the left and 3 doors on the right. Some of the doors are locked and some are unlocked.
Contestants are allowed to try 3 doors and, if they get into a room, to collect the cash prize in
that room. The producer of this show claims that he chooses doors to lock randomly, and always
locks exactly 3 of the doors. An investigator from the network suspects the producer might be
lying, so she views videotape of 200 contestants from the last four years, recording how many
rooms each managed to enter. She obtains the following data:
# doors opened
0
1
2
3
28
69
83
20
a) Do these results support the producer’s claim that he always unlocks exactly three doors
chosen at random ( = .05)?
b) The following year, the investigator records the number of opened doors separately for male
and female contestants, obtaining the following data:
# doors opened
0
1
2
3
Males
22
55
33
9
Females
15
32
73
30
Is there a significant relationship between the number of opened doors and whether a contestant
is male or female ( = .05)?
42. Little Caesars and Dominoes are both trying new plans to speed up delivery. Little Caesars
is equipping their delivery cars with radar detection devices while Dominoes has hired former
professional race car drivers. Below you will find the average delivery time improvements (in
minutes) for the 7 Dominoes and 7 Little Caesars outlets in London from before and after the
new plans have been implemented. Does one of the new plans work better than the other at
improving delivery time ( = .05)?
Little Caesars
Improvement
Outlet 1
Outlet 2
Outlet 3
Outlet 4
Outlet 5
Outlet 6
2
2
-1
1
1
3
Dominoes
Improvement
Outlet 1
Outlet 2
Outlet 3
Outlet 4
Outlet 5
Outlet 6
3
4
6
4
2
0
Outlet 7
2
Outlet 7
5
43. Four meter maids are having an argument about which kind of car is ticketed most often for
illegal parking. To settle the argument, they agree to record the total value of parking fines
assessed for each of three kinds of vehicles – luxury vehicles, compact cars, and minivans. After
recording these values for seven days, they have the following data:
Total value of parking tickets ($)
Meter Maid
Tanya
Trisha
Terri
Talullah
Luxury
90
120
100
110
Compact
70
90
80
70
Minivans
80
90
70
90
a) Based on these scores, does it appear that the types of vehicle differ in average amount of
parking fines ( = .05)?
b) Prior to their collecting the data, the meter maid’s supervisor predicted that luxury cars would
be ticketed for illegal parking more often than compact cars. Do the data above support this
prediction ( = .01)?
44. You’re just about to go on a diet and you’ve got an old bathroom scale to help you figure out
whether the diet is working. The problem is that the scale is so old that it may not be reliable
any more. Now, bathroom scales aren’t particularly reliable anyway, however, they should
show more or less the same weight each time if something is weighed a few times in a row.
Indeed, in the bathroom scale industry, the standard deviation from a number of consecutive
weighings of the same thing should be no more than 1.5 kilos.
a) When you weighed yourself 8 times in succession, the variance in your weights was 9. Is this
evidence that you should dump the scale and buy a new one ( = .05)?
b) After you bought a new scale, you weighed yourself 6 more times in succession. The results
were 60.7, 62.4, 61.9, 60.2, 61.3 and 59.9 kilos. Based on these results, can you conclude that
you no longer weigh 59 kilos, your average weight since high school ( = .01)?
c) Soon after starting your diet, you start going to the gym three times a week where the scale,
supposedly, weighs people heavy. After getting your weight at the gym, you immediately go
home and weigh yourself on your own scale. Over a 10 week period, the weight on your scale is
smaller than the weight on the gym scale 21 times. Based on this result, construct a 98%
confidence interval for the probability that the gym scale will produce a larger weight than your
own scale.
45. At the North American Academic Games, psychologists have dominated the speed events for
years, but engineers have won most of the weight-lifting medals. In the book-lifting competition,
competitors are challenged to lift as many books as they possible can. Historically, engineering
professors have been able to lift a stack of library books containing an average of 37 books, with
a variance of 45.19. In contrast, psychology professors have been able to lift an average of only
27 books, with a standard deviation of 6.8.
a) Before training camp opened last summer, a reporter for Academic Sports Illustrated got a
random sample of 36 psychology professors and 49 engineering professors to lift stacks of
library books. What is the probability that the mean number of books the engineers lifted was at
least 7 books greater than the mean number lifted by the psychologists?
b) This year, the psychology team has been working out, ingesting large quantities of steroids,
and carbo-loading at their campus pubs. The ASI reporter suspects that the difference between
psychologists and engineers has narrowed since the last Games. If in fact the true difference is
now 6.2 books, what is the probability that the reporter draws the correct conclusion if he
samples 35 professors from each discipline and records how much each can lift ( = .05)?
46. In their attempts to discover how West Nile virus is transmitted, researchers have been
collecting mosquitoes throughout Southwestern Ontario. There are essentially three types of
mosquitoes in the area. Forty-five percent of the mosquitoes are Aedes, 40% are Culex and 15%
are Asian Tigers. Researchers have been able to determine that 15% of the Culex mosquitoes
carry the virus, 10% of the Asian Tiger mosquitoes carry the virus and only 2% of the Aedes
mosquitoes carry the virus. Assume that all three types of mosquitoes will bite a person when
given the opportunity..
a) If you are bitten one day and later discover that you did not contract the West Nile virus,
what’s the probability that you were bitten by a Culex mosquito?
b) A team of researchers collected a bunch of dead mosquitoes near a mosquito zapper. There
were 11 Aedes, 3 of which carried the virus, 6 Culex, 2 of which carried the virus and 4 Asian
Tigers, 1 of which carried the virus. Three of the dead mosquitoes were randomly selected and
put into a bag to take back to the lab. What’s the probability that the bag contained no Asian
Tiger mosquitoes?
c) The bag actually contained 3 Aedes mosquitoes, none of which are carrying the virus. The
remaining 18 were divided up into three sets of sizes 7, 6 and 5. What’s the probability that each
set contained exactly 2 mosquitoes that are carrying the virus?
47. At a particular college, students can take an introductory statistics course either by attending
weekly lectures and labs, or by watching videotaped lectures, or simply by reading the text on
their own. You plan to take this course and want to know which, if any, of these options yields
higher average marks. The following are some sample statistics from the common final exam
that all the students in this course wrote last year:
Lectures and labs
n
Mean
Variance
85
71.4
63.7
Videos
43
65.5
71.2
Text only
24
56.7
89.9
a) Is there an overall significant difference between the mean final exam scores of these three
groups ( = .01)?
b) Regardless of your answer in part ‘a’ perform Newmann-Keuls post hoc tests to determine
which groups differ from each other.
ANSWERS
1. a) Z = 2.499, reject HO, b) 50
2. a) t = 1.555, reject HO ; b) F = 15.932, reject HO
3.. F for equal variances = 2.264, do not reject Ho; t = 2.715, Reject HO
4. P(contract settlement/funds adequate) = .50, independent
5. a) 2 = 4.47, do not reject H0; b) 2 = 12.84, reject HO
6. a) 6286; b) 1260; c) .65; d) .462
7. b) 2.251; c) 1.692
8. a) .602; b) .8192; c) 52.68 or 53
9. F =14.71, reject HO; all pairwise comparisons are significant except Group 2 vs. Group 1 (Q’s
= 8.62, 6.77, 5.48, 3.14, 3.63, and 1.86)
10. a) t = 3.72, reject HO; b) 62.54 to 65.96
11. .0853
12. 2 = 23.28, reject Ho
13. a) F = 99.17, reject HO; b) All comparisons significant: Q’s = 19.932, 13.288, and 6.64
14.a) .375; b) .36
15. 4.191 to 7.086
16 F = 24.0, reject HO; T = 61, do not reject HO
17 .062
18 a) Z = -.506, do not reject HO; b) .8420
19 a) r = .961, t = 6.950, reject Ho; b) 21.198  7.91
20 a) .9948; b) Z = - .894, do not reject HO; c) 7.06 to 9.94
21. 2 = 5.574, do not reject HO
22 a) .4272; b) .3966; c) .8966
23b) 3.599, 1.4398
24 a) 2 = 20.898, reject HO; b)2 = 9.50, reject HO; c) 2 = 24.841, reject HO
25. a) .3156, b) .9834
26. a) F = 253.39, reject Ho, b) t = -17.71, reject Ho
27 a) .51, b) .286, c) .12, d) .33
28. a) 2 = 8.66, do not reject Ho, .1485 to .7265
29. F = 40.65, reject Ho of equal variances and do Wilcoxon: T = 70.5, do not reject Ho
30. a) t = .861, do not reject Ho, b) -13.796 to 22.796
31. a) 2 = 6.15, do not reject Ho (male distribution is normal), b) 2 = 3.55, do not reject Ho
(male and female distributions do not differ significantly)
32. a) F = 12.872, reject Ho, b) Tukey Q’s = 3.14 (ns), 7.15 (s), and 4.01 (s) [Qcrit = 3.88]
33. a) r = -.891, t = -4.807, reject Ho, b) 105.04  19.206
34. a) t = 3.706, reject Ho, b) .35 to 12.15
35. a) r = .716, t = 2.512, reject Ho, b) 4.15  7.58, c) t = -19.226, reject Ho
36. a) .0107, b) .9756
37. a) 24.444 to 30.856, b) t = 2.612, reject Ho
38. 2 = 2.467, do not reject Ho, b) 2 = 7.539, do not reject Ho
39. a) F for animals = 195.93, reject Ho; F for training = 90.8, reject Ho; F for interaction = 33.0,
reject Ho, b) N-K Q’s = 4.321, 18.236, and 13.914: all are significant.
40. a) r = .92, t = 5.75, reject Ho, b) 16.885  8.108
41. a) 2 = 47.84, reject Ho, b) 2 = 30.64, reject Ho
42. First do F test for equal variances -> F = 2.44, do not reject Ho, therefore do 2-sample t test > t = -2.242, reject Ho.
43. a) F = 14.72, reject Ho, b) t = 5.092, reject Ho
44. a) 2 = 28.0, reject Ho, b) t = 5.18, reject Ho, c) .505 to .895 (.7  .195)
45. a) .9783, b) .7611
46. a) .371, b) .511, c) .1697
47. a) F = 30.51, reject Ho, b) Q’s = 10.97, 4.40, and 6.57: all are significant