Given name: Family name:
Student number: Signature:
University of Guelph
Department of Economics and Finance
College of Business and Economics
ECON* 2740 (Economic Statistics)
Instructor: Antonie and Maynard
Midterm
VERSION CODE: A
Fall, 2014
Duration: 80 minutes
Aids Allowed: One two-sided handwritten 4 by 6 inch index card formula sheet. Only
simple calculators without programming and scientific functions allowed as determined
by the exam proctors. No other electronic devises permitted.
Answer all questions.
• Multiple choice questions should be answered on the Computer Answer Sheet. All other ques-
tions must include all work on the exam. No credit without work.
• Identify yourself (name and student number) on the Computer Answer Sheet by filling in
the circles.
• Sign your exam, initial each page, and keep your student ID out on the desk in front of you.
• Use only an HB or soft pencil to completely darken the appropriate choice on the answer sheet.
• With the sole exception of simple, non-programable, non-scientific calculators, use of electronic
devices is not permitted. Determination of which calculators are permitted is at the sole
discretion of the exam proctors. Please turn off your cell-phone and all other electronic devices,
placing these together with any personal items at the front of the room.
• You cannot leave the room during the exam without explicit permission from the proctor.
• There are a total of 100 points.
• Hand in your entire exam together with your computer sheet at the end of the exam.
Do not hesitate to raise your hand if you have a question.
Good Luck!
c
⃝Alex Maynard and Luiza Antonie, 2014, all rights reserved
page 2
Long Answer
Please include all your work on the exam. No credit will be given for answers without work,
even when the final answer is correct.
1. The weekly hours for a sample group of 12 employees were as follows:
22 30 32 32 35 36 38 38 38 42 49 51
(a) [3] A statistician has added all 12 data points to obtain a sum of 424. Determine the
sample mean.
(b) [4] Calculate the 25th percentile and interpret its meaning in one clear sentence.
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(c) [5] A statistician has divided the data into three classes: class 1: 22-31, class 2: 32-41,
and class 3: 42-51. Please provide the frequencies, relative frequencies, and cumulative
relative frequencies by filling in the following table:
cumulative
class class relative
frequency relative
name contains frequency
frequency
class 1 22-31
class 2 32-41
class 3 42-51
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2. Netflix is doing market research about two new movies, A and B. They analyzed the viewing
of these movies in a city and observed that during a week 18% of all viewers watched movie A,
12% of all viewers watched movie B, and 10% watched both.
Movie A
Watch Not Watch Marginal Probability
Watch 0.10 0.12
Movie B
Not Watch
Marginal Probability 0.18
(a) [4] Calculate and fill in the missing five probabilities in the table above. If you are com-
pletely stuck, you may raise your hand to irrevocably elect to forgo the points
on this sub-question, including any partial credit, in exchange for obtaining
the answer for use below. This not advised unless you are completely stuck.
(b) [4] What is the probability that a viewer will not watch movie B
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(c) [4] What is the probability that a viewer will not watch any of the movies
(d) [4] What is the probability that a viewer will watch Movie B given that the viewer did
not watch Movie A
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3. The joint probability distribution of X and Y is given by
Y =1 Y =2
X=0 0.20 0.30
X=1 0.30 0.20
(a) [4] Provide the marginal probability distributions for X and Y in the table above. If you
are completely stuck, you may raise your hand to irrevocably elect to forgo
the points on this sub-question, including any partial credit, in exchange for
obtaining the answer for use below. This not advised unless you are completely
stuck.
(b) [4] Solve for expectation or population means of both X and Y
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(c) [5] Solve for the population covariance between X and Y .
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Multiple Choice
Please record all answers on your computer answer sheet using an HB or soft pencil. Be sure to erase
fully.
1. [2] For free point(s), enter the correct version code on your computer answer sheet and mark
the version code on all pages of the test. (Warning: If this information is not correctly entered,
the scantron could miss grade your exam)
Hint: Your version of the exam is version: A
(a) My version of the exam is version A
(b) My version of the exam is version B
(c) My version of the exam is version C
(d) My version of the exam is version D
2. [3] An electronics store is interested in analyzing the sales of the tablets in the last month. The
following frequency distribution was compiled.
Week Sales
1 200
2 300
3 400
4 100
The relative frequency of the sales in the second week is:
(a) 0.50
(b) 0.30
(c) 0.40
(d) 0.27
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3. [3] Using the data from the previous problem, what is the cumulative relative frequency of the
sales by the end of the third week?
(a) 0.40
(b) 0.90
(c) 0.50
(d) 0.35
4. [3] The average starting salary for graduates at a university is 25,000 with a standard deviation
of 2,000. If a histogram of the data shows that it takes on a bell shape, the empirical rule says
that approximately 68% of the graduates would have a starting salary between the following:
(a) 23,000 and 27,000
(b) 21,000 and 29,000
(c) 19,000 and 31,000
(d) 24,000 and 26,000
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5. [3] A study by the Parks Canada revealed that 50% of the vacationers going to the Rocky
Mountain region visit Banff, 40% visit Lake Louise and 35% visit both. What is the probability
that a vacationer will visit at least one of these magnificent attractions?
(a) 0.55
(b) 0.4
(c) 0.7
(d) 0.35
6. [3] Adequate sample size is important to statistical inference in order to:
(a) Reduce the probability that the population will be unrepresentative of the sample due to
nonsampling error.
(b) Reduce the probability that the population will be unrepresentative of the sample due to
sampling error.
(c) Reduce the probability that the sample will be unrepresentative of the population due to
nonsampling error.
(d) Reduce the probability that the sample will be unrepresentative of the population due to
sampling error.
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7. [3] The Ontario Ministry of Education is conducting a detailed survey of student attitudes
towards science. They select 500 high schools at random and survey all of the high school
seniors in each of the 500 schools selected. Their sampling method is best described as:
(a) Random Sampling
(b) Stratified Random Sampling
(c) Cluster Sampling
(d) Observational Sampling
8. [3] Referring again to the information in Question 7, which of the following is the best possible
justification for the sampling method employed.
(a) The Ontario ministry of Education seeks to obtain a sample of students satisfying the
following important property: The fact that one student is chosen as part of the survey
does not effect the chance of another student being chosen.
(b) The Ontario Ministry of Education maintains a list with the contact information of all
the high schools in Ontario, but does not have access to a list or contact information for
Ontario high school students.
(c) The Ontario Ministry of Education seeks to survey the same number of students from
every school in Ontario to ensure that no school is underrepresented.
(d) The Ontario ministry of Education seeks to obtain a survey from a random sample of
Ontario high school students.
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9. [3] If A and B are independent events with P(A) = 0.35 and P(B) =0.60, then P (A|B) is:
(a) 0.25
(b) 0.60
(c) 0.35
(d) 0.80
10. [3] Which of the following statements is most accurate:
(a) When the distribution or histogram is bell-shaped the mean is likely to exceed the median.
(b) When the distribution or histogram is symmetric the mean is likely to exceed the median.
(c) When the distribution or histogram is positive-skewed the mean is likely to exceed the
median.
(d) When the distribution or histogram is negative-skewed the mean is likely to exceed the
median.
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11. [3] A small company has 12 employees, eight men and four women. A four member team is to
be chosen at random for a new project. What is the probability that all four members of the
team will be men?
(a) 1/495 or 0.0020
(b) 1/16 or 0.0625
(c) 1/8 or 0.1250
(d) 14/99 or 0.1414
12. [3] The number of automobiles sold by a dealership in a day is an example of:
(a) a discrete random variable
(b) a constant
(c) the Bernoulli probability distribution
(d) the binomial probability distribution
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13. [3] Your friend shares the following rumor about the last midterm:
It was easy: sixty percent of the students scored more than two points above the
median
Choose the most accurate statement below:
(a) Although implausible, the rumor is statistically possible if the histogram is positive skewed.
(b) Although implausible, the rumor is statistically possible if the histogram is negative skewed.
(c) Although implausible, the rumor is statistically possible if the histogram is bell-shaped.
(d) The rumor is not only implausible, the rumor is statically impossible
14. [3] Cold winter nights can be deadly for Toronto’s homeless. A researcher seeks to understand
why some of Toronto’s homeless choose not to sleep in shelters even on cold nights. She surveys
a random sample of homeless people staying at shelters across the city and asks them to rate
their satisfaction with the city’s homeless shelters on a scale of 1-10. Select the most accurate
completion of the critique below:
Critique of homeless shelter study:
This is not a random sample of Toronto’s homeless population because
(a) not all of Toronto’s homeless have an equal chance of being chosen. The results
will likely overstate
(b) not all of Toronto’s homeless have an equal chance of being chosen. The results
will likely understate
(c) the fact that one survey participant is chosen is likely to effect the probability
that another participant is chosen. The results will likely overstate
(d) the fact that one survey participant is chosen is likely to effect the probability
that another participant is chosen. The results will likely understate
the satisfaction of the city’s homeless population with the shelters provided.
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15. [3] P (A|AC ) is closest or equal to:
(a) 0
(b) 0.5
(c) 1
(d) The information provided is insufficient to determine the answer.
16. [3] Suppose that X and Y are random variables, with E[X] = 5, and E[Y ] = 4. Then
E[2X + 3Y + 8] is closest or equal to:
(a) 22
(b) 30
(c) 56
(d) 64
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17. [3] Referring to the same random variables as in question 16, suppose we are also told that
the variances and covariance are given by V (X) = 9, V (Y ) = 4 and COV (X, Y ) = −3. Then
V AR(2X + 3Y + 8) is closest or equal to:
(a) 18
(b) 36
(c) 44
(d) 72
18. [3] A mortgage holding company has found that 2% of its mortgage holders default on their
mortgage and lose the property. Furthermore, 90% of those who default are late on at least
two monthly payments over the life of their mortgage as compared to 45% of those who do not
default. What is the joint probability that a mortgagee has two or more late monthly payments
and does not default on the mortgage?
(a) 0.432
(b) 0.441
(c) 0.018
(d) 0.034
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19. [3] In the small town of Doverpants, all eight hundred men wear pants in compliance with the
traditional social norms of Doverpants, whereas women may wear either pants or dresses. A
recent survey of all one thousand female residents of Doverpants showed that on any given day
half of the women in Doverpants will wear pants and the other half will wear dresses. You meet
a random resident of Doverpants. The probability that he or she is wearing pants is closest or
equal to:
(a) 5/9 or 0.556
(b) 8/13 or 0.6154
(c) 13/18 or 0.722
(d) 10/13 or 0.769
20. [3] Refer again to the information in question 19. You meet a random pant-wearing resident of
Doverpants. The probability that the pant-wearing resident is male is closest or equal to:
(a) 5/9 or 0.556
(b) 8/13 or 0.6154
(c) 13/18 or 0.722
(d) 10/13 or 0.769
END OF EXAM
End of examination
Total pages: 17
Total marks: 100
