STAT*2040 W12
Test 1 (White Version)
February 15 2012
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University of Guelph
Department of Mathematics and Statistics
STAT*2040
Statistics I
Test 1 (White version)
February 15 2012
Examiner: Jeremy Balka
This exam is 70 minutes in duration
Name:
ID:
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Please read the instructions:
1. Fill out your name and ID number above.
2. When the examination starts, make sure your question paper is complete. You should have 22
multiple choice questions, along with a formula sheet and standard normal tables. The first
question is just a bookkeeping question, and does not count for marks, but please fill it in to ensure
your exam is properly graded.
3. Do all rough work on this paper.
4. You are allowed to bring in a calculator, and pens and pencils.
5. There is only one correct answer for each question. Fill in only one bubble for each question.
6. Fill out the computer answer sheet in pencil as you go. There will be no extra time given at the
end of the exam to fill in the sheet.
7. The answers given in the exam are often rounded versions of the correct answer. Choose the
closest value.
1. The colour of the first page of this examination booklet (the cover sheet) is:
(a) White
(b) Yellow
2. A study investigated the effect of a regular dose of aspirin on the risk of strokes. Physicians
randomly assigned approximately 5,000 volunteers to a group that took an aspirin every second
day, and 5,000 to a control group that took a placebo instead. The volunteers were followed
for several years, and researchers compared the rate of strokes in the two groups. Consider the
following statements.
I. This is an experiment, not an observational study.
II. The response variable is aspirin use.
III. This type of study cannot possibly yield evidence of a causal link between aspirin use and
rate of strokes.
Which of these statements are true?
(a)
(b)
(c)
(d)
(e)
Just I.
I and III.
II and III.
All of them.
None of them.
3. Consider the following sample of 4 observations: −8, 12, 16, 31.
What is the value of the sample variance?
(a)
(b)
(c)
(d)
(e)
11
16
29
112
258
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4. If all observations in a data set have 10 added to them, how many of the following quantities would
change in value?
x̄, s, Q1 , IQR, 10th percentile.
(a)
(b)
(c)
(d)
(e)
1
2
3
4
5
5. Which one of the following statements is true?
(a) For right-skewed distributions, the median is greater than the mean.
(b) For mound-shaped distributions, approximately 50% of observations lie within 5 standard
deviations of the mean.
(c) For any distribution, the interquartile range is equal to 50.
(d) If the range of a data set is equal to 0, the variance and IQR will also equal 0.
(e) None of the above.
6. A human resources administrator in a large company is interested in estimating the average age
of new hires. The administrator looks at an alphabetical list of 200 new hires, and picks the first
30 names on the list. They find the average age of these 30 people is 28.2. Consider the following
statements.
I. This is an experiment, not an observational study.
II. The number 28.2 is a statistic, not a parameter.
III. The 30 people represent a simple random sample from the population of interest.
Which of these statements are true?
(a)
(b)
(c)
(d)
(e)
Just II.
I and II.
I and III.
II and III.
None of them.
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7. A new mother and father bring their 2 month old baby in to see their doctor for a check-up. The
doctor measures the baby’s length in centimetres, and tells the parents that in terms of length of
babies that age, their baby’s z-score is −2.0. Which one of the following statements is true?
(a)
(b)
(c)
(d)
The
The
The
The
units of the z-score are centimetres.
baby’s length is 2 centimetres less than the mean length of babies that age.
baby’s length is greater than 50% of babies that age.
baby’s length is 2 standard deviations less than the mean length of babies of that age.
8. Is there a relationship between fatty fish consumption and the rate of prostate cancer? A study
followed 6272 Swedish men for 30 years. They were categorized according to their fish consumption,
and to whether they developed prostate cancer. The following table summarizes the results.
Fish consumption
Never/seldom Small Moderate Large
Prostate cancer
14
201
209
42
No prostate cancer
110
2420
2769
507
If one of these 6272 men is randomly selected, what is the probability their fish consumption was
large or moderate, given they did not get prostate cancer?
(a)
(b)
(c)
(d)
(e)
0.48
0.52
0.56
0.60
0.64
9. Let A be the event that a randomly selected Canadian is at least 20 years old. Let B be the event
that a randomly selected Canadian has a driver’s license. Which one of the following statements
is true?
(a)
(b)
(c)
(d)
(e)
P (A|B) < P (A).
P (B|A) > P (B).
A and B are mutually exclusive.
A and B are independent.
None of the above.
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10. Consider the following probability distribution of a random variable X.
x
2
4
6
p(x) 0.10 0.10 0.20
8
?
One of the probabilities in the table is missing. Find the missing probability, then calculate the
mean of X. What is the mean of X?
(a)
(b)
(c)
(d)
(e)
4.8
5.0
5.6
6.2
6.6
11. In Canada, approximately 10% of people with diabetes have Type I diabetes. Suppose 15 people
in Canada with diabetes are randomly sampled. What is the probability that no more than 1 has
Type I diabetes?
(a)
(b)
(c)
(d)
(e)
0.21
0.34
0.38
0.42
0.55
12. Consider again the information in the previous question. If 15 people with diabetes are randomly
sampled, what is the probability exactly one has Type I diabetes, given at least one has Type I
diabetes?
(a)
(b)
(c)
(d)
(e)
0.34
0.43
0.55
0.62
0.69
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13. A small town has two different taxi companies: Kevin’s Kab and Terry’s Taxi. Kevin’s Kab
accounts for 70% of taxi trips in the town, and Terry’s Taxi accounts for the other 30%. On a
Kevin’s Kab trip, there is a 10% chance the customer will be overcharged. On a Terry’s Taxi trip,
there is a 29% chance the customer will be overcharged. Suppose on a randomly selected taxi trip
the customer was overcharged. What is the probability this trip was in a Terry’s Taxi taxi?
(a)
(b)
(c)
(d)
(e)
0.30.
0.40.
0.45.
0.50.
0.55.
14. Suppose in a certain rough neighbourhood, the number of armed robberies at a local convenience
store approximately follows a Poisson distribution with a mean of 1.8 per month. In a randomly
selected month, what is the probability there is at least one robbery?
(a)
(b)
(c)
(d)
(e)
0.30
0.57
0.72
0.77
0.83
15. None of the random variables in the following situations have a binomial distribution. But the
distribution of one of them can be reasonably approximated by a binomial distribution. Which
one?
(a) The number of kings drawn when 45 cards are drawn without replacement from a standard
deck.
(b) The number of males in a simple random sample of 500 faculty members at the University
of Guelph.
(c) The length of time between deaths at an emergency room at a hospital.
(d) The height of people in a random sample of 1,000,000 adult Canadians.
(e) The number of male students in a simple random sample of 4 medical students at a large
medical school.
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16. A machine fills cereal boxes at a cereal producing plant. The amount of fill put in a box is
approximately normally distributed, with a mean of 520.0 grams and a standard deviation of 5.0
grams. If 4 of these boxes are randomly and independently sampled, what is the probability that
exactly 1 has less than 510.0 grams of cereal in it?
(a)
(b)
(c)
(d)
(e)
0.00003
0.02
0.05
0.09
0.11
17. Let X have a continuous uniform distribution on the interval (510, 540). What is P (X > 528.0|X < 530.0)?
(a)
(b)
(c)
(d)
(e)
0.1
0.2
0.3
0.4
0.5
18. Suppose P (A) = 0.20, P (B) = 0.75, and P (B|A) = 0.25. Which one of the following statements
is true?
(a)
(b)
(c)
(d)
(e)
P (Ac ∩ B) = 0.70.
P (A|B) = 0.20.
P (A ∩ B) = 0.20
P (A ∪ B) = 0.95.
None of the above.
19. Which one of the following statements is true?
(a)
(b)
(c)
(d)
(e)
If Z has the standard normal distribution, then P (Z = 0) = 0.50.
The height of a density curve, f (x), is a probability.
The height of a density curve, f (x), can be less than 0.
A standard normal random variable cannot take on a value greater than 10.
None of the above.
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The next several questions refer to the following information.
At a certain fish farm, 2.5 year-old salmon have weights that are approximately normally distributed with a mean of 5.30 kg and a standard deviation of 0.25 kg.
20. If one 2.5 year-old salmon from this farm is randomly selected, what is the probability its weight
lies between 5.30 and 5.55 kg?
(a)
(b)
(c)
(d)
(e)
0.17
0.34
0.37
0.44
0.84
21. What is the 60th percentile of the weight of 2.5 year-old salmon at this farm?
(a)
(b)
(c)
(d)
(e)
5.26
5.32
5.36
5.40
5.44
22. If nine 2.5 year-old salmon from this farm are randomly selected, what is the probability their
mean weight is greater than 5.22 kg?
(a)
(b)
(c)
(d)
(e)
0.16
0.54
0.67
0.73
0.83
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