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University of Guelph
Department of Economics and Finance
College of Business and Economics
ECON* 2740 (Economic Statistics)
Instructor: Maynard
Midterm
VERSION CODE: B
Fall, 2015
Duration: 120 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 questions 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.
• The total marks are provided on the back of your exam. Your grade on the exam will be based on the percentage of correct marks.
• 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, 2015, all rights reserved

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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 following sample of data on education and years of schooling were recorded, where annual income is measured in thousands of dollars and education is measured in years of schooling. respondent 1
2
3
4
5

Income
51
15
62
68
77

Education
8
5
16
6
16

NOTE: For the answers to Question 1 below you may round to two digits of accuracy, such as rounding 1.5478 to 1.55.
(a) [5] Provide the median income and education

(b) [5] Find the sample mean of both income and education. Denote them clearly and circle your answers.

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(c) [5] Find the sample standard deviation of both income and education. Denote them clearly and circle your answers.

(d) [5] Find the covariance of income and education. Circle your answer.

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(e) [4] calculate a statistic that tells you how much of the variation in income can be explained
(or accounted for) by variation in education?

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2. A (small) random sample of Canadian voters were polled ahead of last Monday’s election to determine both their party preferences and the issues they felt most important to them. To keep this purely fictional opinion poll manageable for the sake of students taking the midterm exam, only three major parties and three major issues were discussed. No political judgement of any kind is intended with respect to the parties, issues, or fictional poll results.
The data were coded as follows. For political party: 1 = Conservative, 2= Liberal, 3 = NDP.
For Issues: 1 = Economic Policy 2 = Environment and Resources, and 3 = Immigration and
Foreign Policy
The results from the survey were recorded as follows:
Voter
1
2
3
4
5
6
7
8
9

Party
1
3
1
2
3
2
1
2
3

Issue
1
2
3
1
3
2
1
2
2

(a) [4] Fill in the table below to show the frequency and relative frequency of the issues that voters in this sample consider their top priority.

Issue
Economic Policy
Environment and Resources
Immigration and Foreign Policy

Frequency

Relative Frequency

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(b) [3] Provide a bar chart showing the frequency from Question 2a and a pie chart showing the relative frequency from Question 2a. Be sure to label clearly. The figures do not have to be drawn exactly to scale and you do not need to be an artist.

(c) [4] Provide a cross classification table of frequencies with party affiliation in the rows by filling in the table below

Economic
Policy

Environment
Reserouces

Immigration &
Foreign Policy

Conservative
Liberal
NDP

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(d) [4] Fill in the table below to provide the relative frequency with which a voter supporting each of three parties lists a given issue as their top priority. For example, we should be able to look up the relative frequency with which a liberal voter lists the economy as their top priority.

Economic
Policy

Environment
Reserouces

Immigration &
Foreign Policy

Conservative
Liberal
NDP

(e) [4] Fill in the table below to provide the relative frequency with which a voter listing each of the three issues as their top priority supports a given party. For example, it should tell you the relative frequency with which a voter listing the economy as her top priority supports the liberal party.

Economic
Policy

Environment
Reserouces

Immigration &
Foreign Policy

Conservative
Liberal
NDP

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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. [3] 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: B
(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] All of the following are indications that the histogram is not bell shaped, EXCEPT
(a) The histogram is bimodal
(b) the histogram is unimodal
(c) The histogram is positively skewed
(d) The histogram is negatively skewed

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3. [3] One thousand grade 8 students will take an end-of-year exam. Any student who does not obtain at least a 30 on the exam will be required to repeat grade 8 again next year. Any student who obtains above 90 will skip grade 9 and proceed directly to grade 10. All other students will be enrolled in grade 9. Suppose that the mean on the exam is 60, the standard deviation is 10, but the distribution is not symmetric. Which is the most precise statement: Of these one thousand students,
(a) at least 750 will enroll in grade 9.
(b) at least 888 will enroll in grade 9.
(c) at least 950 will enroll in grade 9
(d) at least 997 will enroll in grade 9

4. [3] Referring to the Question 2 of the long answer section, your friend is skeptical that such a small sample size can give us a reliable indication of voter intentions for the population at large. Which best describes all of your friend’s concern(s) as stated above? [Note you do not need to complete the long answer question to answer this problem]
(a) This is not a true random sample
(b) The sample may not reflect the population due to non-sampling error
(c) The sample may not reflect the population due to sampling error
(d) Both 4b and 4a.

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5. [3] Referring to the Question 2 of the long answer section, suppose that the response rate for your survey was only thirty percent. Your aunt believes, for reasons unexplained, that voters supporting the liberal party will be less likely to respond to the survey than voters supporting the other two parties. For this reason she is skeptical that your sample was collected in a way that gives us a reliable indication of voter intentions for the population at large. Which best describes all of your aunt’s concern(s) as stated above? [Note you do not need to complete the long answer question to answer this problem]
(a) This is not a true random sample
(b) The sample may not reflect the population due to non-sampling error
(c) The sample may not reflect the population due to sampling error
(d) Both 5b and 5a.

6. [3] Which of the following is the most accurate statement. Please read each statement carefully.
(a) The significance level is an indication of how likely the conclusions drawn from the sample statistics can be accurately applied to the population parameters.
(b) The confidence level is an indication of how likely the conclusions drawn from the sample parameters can be accurately applied to the population statistics.
(c) The significance level is an indication of how likely the conclusions drawn from the population parameters can be accurately applied to the sample statistics.
(d) The confidence level is an indication of how likely the conclusions drawn from the sample statistics can be accurately applied to the population parameters.

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7. [3] Data set 1 contains a hundred observations with values ranging from -40 to 270. Data set
2 contains three hundred observations with values ranging from 23 to 86. The mean for Data set 1 is far above its median. The mean of Data set 2 is equal to its median. We wish to provide a histogram for both data sets. Which data set should be divided into a larger number of classes in order to construct the histogram according to method of selecting the number of classes discussed in lecture.
(a) Impossible to determine given the information provided
(b) Equal number for both data sets
(c) Data Set 1
(d) Data set 2

8. [3] In an effort to deter international tax evasion, the Canadian Revenue Agency has recently increased reporting requirements with high non-compliance penalties for certain foreign property holdings. An advocacy group for immigrants is concerned that recent immigrants, some of whom may still hold property in their country of origin for non-tax reasons, could be disproportionately affected by the new requirement. Let A denote the event that a randomly selected Canadian taxpayer is a recent immigrant and let B denote the event that they own foreign property. The advocacy group’s concern is best represented by which of the following inequalities: (a) P (A|B) > P (B|A)
(b) P (B|A) > P (B|AC )
(c) P (B|A) > P (A|B)
(d) P (A|B) > P (A|B C )

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9. [3] Referring to question 8. After substantial research, the advocacy group has determined the following (fictional) table of joint probabilities.
A
AC

B
0.05
0.10

BC
0.05
0.80

According to the table above the margin probability of holding foreign property is closest or equal to:
(a) 0.5 0
(b) 0.15
(c) 0.10
(d) 0.05

10. [3] Referring to Questions 8 and 9, the probability that a randomly selected taxpayer is a recent immigrant who owns foreign property is closest or equal to:
(a) 0.33
(b) 0.15
(c) 0.10
(d) 0.05

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11. [3] Referring to Questions 8 and 9, if a taxpayer is a recent immigrant, the probability that they hold foreign property is closest or equal to:
(a) 0.50
(b) 0.33
(c) 0.15
(d) 0.05

12. [3] You roll a fair four-sided die twice, with sides numbered 1,2,3 & 4, shaking it well each time before rolling. The probability that you roll two 4s is closest or equal to:
(a) 0.2500
(b) 0.1875
(c) 0.1250
(d) 0.0625

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13. [3] Referring to the information in Question 12, let A be the event that your first role is strictly less than 4 and B be the event that your second role is strictly greater than 1. Then P (A or B) is closest or equal to:
(a) 0.9375
(b) 0.8125
(c) 0.5625
(d) 0.5000

14. [3] Referring to the information in Question 12, Let A be the event that your first role is strictly less than 4 and B be the event that your second role is strictly greater than 1. Then P (A|B) is closest or equal to:
(a) 0.8000
(b) 0.7500
(c) 0.6666
(d) 0.5625

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15. [3] Referring to the information in Question 12, let X be the random variable taking the value of the first role. The population mean of X is closest or equal to.
(a) 3.0
(b) 2.5
(c) 2.0
(d) 1.5

16. [3] Referring to the information in Question 12, let Y equal the sum of the two rolls. The population mean of Y is closest or equal to.
(a) 5.5
(b) 5.0
(c) 4.5
(d) 4.0

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17. [3] In a double header, a teams probability of winning the first game is 0.55. If the teams loses their first game, then their probability of winning the second game drops to 0.40, whereas if they win the first game, then it rises to 0.70. There are no ties. The probability that the team wins the second game is closest or equal to:
(a) 0.627
(b) 0.605
(c) 0.565
(d) 0.535

18. [3] Refer to the information in Question 17. The team has won the second game. The probability that they lost the first game is closest or equal to:
(a) 0.2975
(b) 0.31858
(c) 0.33645
(d) 0.50222

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19. [3] In a best out of seven game competition, your team must win at least four games to win the competition. Suppose that the probability of your teaming winning each game is 0.60 and that the outcome (win or lose) of each game is independent of the outcome of every other game.
Given that your team has lost the first three games, the probability that your team will win the next four is closest or equal to:
(a) 0.1296
(b) 0.0625
(c) 0.0576
(d) 0.0256

END OF EXAM
End of examination
Total pages: 17
Total marks: 100