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UNIVERSITY OF TORONTO Faculty of Arts and Science

AUGUST 2015 EXAMINATIONS

ECO220Y1Y

Duration - 3 hours

Examination Aids: A non-programmable calculator

This exam includes these pages and a separate BUBBLE FORM. Once the exam begins, please detach the 7-page Attachment from the end of this exam. The Attachment includes your formula sheets, statistical tables (Standard Normal, Student and ), as well as graphs, tables, and other information needed to answer some exam questions. Anything written on the Attachment will not be graded. You are responsible for turning in both the BUBBLE FORM and all 18 pages of this exam. You must complete both, including entering your name and student number, before the end of the exam is announced.

This exam has two parts plus the Attachment. Part 1 is open-ended questions. Write your answers to Part 1 on these exam papers. Part 2 is multiple choice questions. You must record your answers to Part 2 on the BUBBLE FORM. In ALL cases what is (or is not) marked on the BUBBLE FORM is your answer. Marks for Part 2 are based SOLEY on the BUBBLE FORM, which you must complete before the end of the exam is announced.

Part 1: Three (3) written questions with varying point values worth a total of 70 points. Write your answers clearly, concisely, and completely below each question. Make sure to show your work and reasoning. Make sure your graphs are fully labeled. A guide for your response ends each question to let you know what is expected: e.g. a quantitative analysis, a graph, and/or sentences. Unless otherwise specified, you choose the significance level. (If there are no special considerations, you may choose a 5% significance level.)

Part 2: Twenty four (24) multiple choice questions with point values from 1 to 2 points each for a total of 40 points.

Surname (last name):

Given name (first name):

Student #:

Q1 Q2 Q3 Part 1 Total

Part 2 Total

Raw Total

Percent Mark

Point Value: 15 20 35 70 40 110

Points Earned:

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Part 1. Short Answers. Show your work in each question. (1) [15 pts] Suppose that a lightbulb manufacturing plant produces bulbs with a mean life of 2000 hours and

a standard deviation of 400 hours. An inventor claims to have developed an improved process that produces bulbs with a longer life and the same standard deviation. The plant manager randomly selects 100 bulbs produced by the process and uses the following

Testing procedure: Conclude the inventor’s claim if the sample mean life of the bulb is greater than 2100 hours; otherwise conclude that the new process is no better than the old process.

Let denote the mean life of the lightbulbs from the new process. The null and alternative

hypotheses are 2000:0 H vs. 2000: aH .

(a) [5 pts] What is the significance level of the plant manager’s testing procedure?

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(1) (continued) (b) [5pts] Suppose the new process is in fact better and has a mean bulb life of 2150 hours. What is

the power of the plant manager’s testing procedure?

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(1) (continued) (c)[5pts] What testing procedure should the plant manager use if she wants the significance level of

her test to be 5%?

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(2) [20pts] Data were collected from a random sample of 127 house sales from a city. Let Price = the selling price (in $1000) BDR = the number of bedrooms Bath = the number of bathrooms Hsize = size of the house (in square feet) Lsize = lot size (in square feet) Age = age of the house (in years)

Poor =

otherwisepoorasreportedishousetheofconditiontheif

0

""1

An estimated regression yields

PoorAgeLsizeHsizeBathBDRice

8.48090.0002.0156.04.23485.02.119Pr (23.9) (2.61) (8.94) (0.011) (0.00048) (0.311) (10.5)

6.02 R ; .900)(Pr iceVar

where the numbers in parentheses are the standard errors of the corresponding regression coefficients. (a) [2pts] Suppose that a homeowner converts part of an existing family room in her house into a new

bathroom. What is the expected increase in the price of the house? (b) [3pts] Suppose that a homeowner adds a new bathroom to her house, which increases the size of

the house by 100 square feet. What is the expected increase in the price of the house? (c) [1pt] What is the loss in price if a homeowner lets her house run down so that its condition becomes

“poor”?

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(2) (continued) (d) [2pts] The coefficient of BDR is 0.485. Interpret its meaning in one or two sentences. (e) [2pts] Interpret the meaning of the coefficient for Poor in one or two sentences. (f) [5pts] Test the overall significance of the model at 5% significance level. You must write down the null and alternative hypotheses, the decision rule, value of the test statistics and the conclusion.

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(2) (continued) (g) [5pts] Test the significance of each explanatory variable at 5% significance level.

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(3) [35 pts] Refer to Table 1 in the Attachment [from “The Homecoming of American College Women: The

Reversal of the College Gender Gap”, by Goldin, Katz and Kuzienko (Journal of Economic Perspectives—Volume 20, Number 4—Fall 2006—Pages 133–156) ]

(a)[5pts] The difference between column 1 and column 2 is that the regressions in column 2 include controls for family background, such as parental income, mother’s education, race, and ethnicity. Explain why the authors would need to control for those characteristics in order to estimate the gender gap.

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(3) (continued) (b)[8 pts] Interpret the coefficient on “Female” in column 2. Compare each cohort of graduates and

discuss how this relates to the main questions the authors are trying to answer.

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(3) (continued) (c)[10 pts] Fully interpret column 5 of Table 1 for the 1992 graduates.

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(3) (continued) (d)[12 pts] The authors claim that: “Whereas almost none of the gender gap favoring males could be explained for the 1957 and

1972 graduating classes, about 40 percent of the female advantage can be explained through the combined impacts of test scores, grades, and courses in 1992.”

Based on the results of Table 1, in particular comparing columns 2 and 5 for each cohort, evaluate that claim.

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Part 2. Multiple Choice Questions. No part mark.

Twenty four (24) multiple choice questions with point values from 1 to 2 points each for a total of 40 points. Point value for each question shown by [1pt] or [2pts]. Most questions have choices (A) – (E). For questions with fewer choices, the correct answer is ALWAYS one of those offered (e.g. if the choices are (A) – (D), then (E) is NOT a possible correct answer.) You must record your answers to Part 2 on the BUBBLE FORM.

On the FRONT of the BUBBLE FORM: Print your 9 (or 10) digit student number in the boxes AND darken each number in the corresponding circles; Print your last name and initial in the boxes AND darken each letter in the corresponding circles; You may leave the FORM CODE blank.

On the BACK of the BUBBLE FORM: Write in your name, sign, and record your answers. Use a pencil and make dark solid marks that fill the bubble completely. Erase completely any marks you want to change; Crossing out a marked box is incorrect. Choose the best answer for each question. If multiple answers are indicated, that question earns 0 points. For questions with numeric answers that require rounding, round your final answer to be consistent with

the choices offered. Use standard rounding rules.

REMEMBER, you must record your answers to these 24 multiple-choice questions on the BUBBLE FORM.

Questions (1) – (2): In summer 2014, Harvard and MIT released de-identified student data on 16 massive open online courses (MOOCs): MITx and HarvardX, 2014, “HarvardX-MITx Person-Course Academic Year 2013 De-Identified dataset, version 2.0,” http://dx.doi.org/10.7910/DVN/26147. Over 600,000 students from around the world signed up for these 16 courses (in total) in the 2012/13 academic year. This includes 10,208 students from Canada, 156,107 from the U.S.A., 78,200 from India, 7,123 from Nigeria, and 3,646 from China (and many from other countries). Consider this graphical summary of one variable in these data.

(1) [1pt] For which country is the 75th percentile the largest (oldest)?

(A) Canada (B) China (C) India (D) Nigeria

(2) [1pt] What is the shape of the student age distribution in the U.S.A.?

(A) negatively (left) skewed (B) positively (right) skewed (C) approximately Uniform (D) approximately Student (E) approximately Normal (Bell shaped)

0 20 40 60 80Student Age

U.S.A.

Nigeria

India

China

Canada

Age of MOOC students by origin country

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Questions (3) – (6): “Retail Sales: A Study of Pricing Behavior in Supermarkets” published in 2002 by the Journal of Business looks at price variation for two major brands of ketchup: Heinz and Hunt’s. Here is a table from that paper with somewhat altered numbers (to simplify things). Percent of days reports the percent of days that the ketchup was sold at each price (e.g. if during 100 out of 1000 days the price was set at $0.99 then that is 10% of days). Percent of units sold reports what percent of all bottles sold were sold at each price (e.g. if out of 1 million bottles sold, 100,000 were sold at $0.99 then that is 10% of units sold).

Distribution of Prices

Price: Heinz

$0.79 $0.99 $1.19 $1.39 $1.49 Percent of days 2 14 17 24 43 Percent of units sold 13 37 20 8 22

Price:

Hunt’s$0.99 $1.09 $1.19 $1.39 $1.49 $1.79

Percent of days 9 3 17 27 38 6Percent of units sold 40 6 21 10 21 2

(3) [1pt] If you randomly select a day, what is the expected selling price of Heinz ketchup?

(A) $1.17 (B) $1.19 (C) $1.25 (D) $1.29 (E) $1.33

(4) [1pt] If you randomly select a bottle of ketchup sold, what is the expected selling price of Heinz?

(A) $1.15 (B) $1.18 (C) $1.22 (D) $1.25 (E) $1.28

(5) [1pt] Considering the distribution of Hunt’s selling prices over days, what is the median?

(A) $1.19 (B) $1.24 (C) $1.29 (D) $1.39 (E) $1.49

(6) [1pt] Considering all four price distributions, which has the largest 15th percentile?

(A) Heinz price distribution over days (B) Heinz price distribution over units sold (C) Hunt’s price distribution over days (D) Hunt’s price distribution over units sold

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Questions (7) – (9): Consider this unlabelled graph of the sampling distribution of a sample proportion.

(7) [2pts] For which of these scenarios could the graph above show the sampling distribution of ?

(A) = 30 and = 0.1 (B) = 100 and = 0.2 (C) = 1000 and = 0.001 (D) = 1000 and = 0.999 (E) All of the above

(8) [2pts] If = 2000 and = 0.74, which value belongs at the point marked “?” in the graph?

(A) 0.75 (B) 0.76 (C) 0.77 (D) 0.78 (E) 0.79

(9) [2pts] If = 950 and = 0.11, which value belongs at the point marked “??” in the graph?

(A) 0.04 (B) 0.05 (C) 0.06 (D) 0.07 (E) 0.08

Questions (10) – (13): In 2014 Gallup surveyed a random sample of 29,560 people in the U.S. with a four-year degree or higher who graduated between 1990 and 2014: “Student Debt Linked to Worse Health and Less Wealth” (http://www.gallup.com/poll/174317/student-debt-linked-worse-health-less-wealth.aspx). Questions asked about well-being and student loan debt. Well-being includes purpose (“liking what you do each day and being motivated to achieve your goals”) and physical (“having good health and enough energy to get things done daily”). For each, respondents are classified as thriving, struggling or suffering.

?? ? Sample Proportion ( )

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Percentage of U.S. University Graduates Thriving in These Elements of Well-Being by Amount of Student Loan Debt No student debt $25,000 and below $25,001 to $50,000 Over $50,00Purpose 49 46 40 40Physical 34 30 26 24 Student Loan Debt Among U.S. University Graduates Who Graduated Between 1990 and 2014 Approximately how much money did you borrow in student loans to obtain your undergraduate degree at (name of institution)? %No student debt 41$25,000 and below 27$25,001 to $50,00 21Over $50,000 11

(10) [1pt] What kind of data did Gallup collect?

(A) observational, time series data (B) observational, cross-sectional data (C) observational, panel (longitudinal) data (D) experimental, time series data (E) experimental, panel (longitudinal) data

(11) [2pts] If you randomly select 3 people from the 29,560, what is the chance 2 have no student debt?

(A) 0.07 (B) 0.10 (C) 0.17 (D) 0.20 (E) 0.30

(12) [2pts] What is the standard error associated with 49% (from the first row of results in the top table)?

(A) 0.3% (B) 0.5% (C) 0.7% (D) 0.9% (E) 1.1%

(13) [2pts] Looking at the first row of results in the top table, what are the hypotheses to test if the difference between 49 and 40 is statistically significant?

(A) : = 0 and : ≠ 0 (B) : − = 0 and : − ≠ 0 (C) : − = 0 and : − ≠ 0 (D) : − = 0 and : − ≠ 0 (E) : − = 0 and : − ≠ 0

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Questions (14) – (16): Suppose x is the height of a CEO in cm and y is total annual compensation in hundreds of thousands of dollars ($100,000s). For a random sample of 42 CEO’s a regression of the natural log of compensation on height yields these OLS results:

ln(y)-hat = -2.635 + 0.029*x; n = 42; R-squared = 0.089

(14) [2pts] How should you interpret 0.029?

(A) On average, CEOs with salaries that are 1 percent higher are 0.029 cm taller (B) On average, CEOs who are 1 cm taller have salaries that are $2,900 higher (C) On average, CEOs who are 1 cm taller have salaries that are 2.9 percent higher (D) On average, CEOs who are 1 percent taller have salaries that are $2,900 higher (E) On average, CEOs who are 1 percent taller have salaries that are 2.9 percent higher

(15) [2pts] What would happen if height were measured in inches? (Note: 1 cm = 0.3937 inches)

(A) The OLS intercept would change to -1.037 and the OLS slope would change to 0.011 (B) The OLS slope would stay the same (0.029) but the OLS intercept would change to -1.037 (C) The OLS slope would stay the same (0.029) but the OLS intercept would change to -6.693 (D) The OLS intercept would stay the same (-2.635) but the OLS slope would change to 0.011 (E) The OLS intercept would stay the same (-2.635) but the OLS slope would change to 0.074

(16) [2pts] What would change if compensation were measured in millions of dollars (but everything else was the same as in the original regression)?

(A) Only the OLS slope would change (B) Only the OLS intercept would change (C) Both the OLS slope and intercept would change (but not the R2) (D) Everything would change: the OLS slope, the OLS intercept, and the R2

(E) Nothing would change: the OLS slope, OLS intercept, and R2 would stay the same

Questions (17) – (18): The Public Opinion Analysis sector monitors public opinion in the EU to help inform communications and decisions: http://ec.europa.eu/public_opinion/index_en.htm. In February 2015 it published a report “Cyber Security,” based on surveys in each member state. Consider one question and the replies in Italy and France. In Italy, 54% of the 1,019 people surveyed said they use the Internet every day (the other options were often, sometimes, and never). In France, 76% of 1,011 people said every day. (17) [2pts] Using a 1% significance level, what is the margin of error for the French estimate?

(A) 2.9% (B) 3.1% (C) 3.5% (D) 4.1% (E) 4.4%

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(18) [2pts] Using a 10% significance level, what is the margin of error for the difference between the Italian and French estimates?

(A) 3.0% (B) 3.2% (C) 3.4% (D) 3.7% (E) 4.0%

Questions (19) – (20): A random sample of 100 observations is selected from a population with mean and standard deviation =10. We wish to test 10:0 H verses 10:1 H at a significance level , where is the mean of the population. (19) [1pt] If a 95% confidence interval for is (8.5, 11.6), which one of the following statements is

true? (A) Reject 0H at both =0.05 and =0.01. (B) Fail to reject 0H at both =0.05 and =0.01. (C) Fail to reject 0H at =0.05 but not necessarily at =0.01. (D) Fail to reject 0H at =0.05 but not necessarily at =0.01. (E) None of the above is true.

(20) [2pts] If the p-value of the test is 0.035, which one of the following statements is true? (A) Reject 0H at both =0.05 and =0.01.

(B) Do not reject 0H at both =0.05 and =0.01. (C) Reject 0H at =0.05 but do not reject at =0.01.

(D) Do not reject 0H at =0.05 but reject at =0.01. (E) None of the above is true.

Questions (21) – (22): To compare the proportion of people who support a certain government policy, two independent random samples are selected from Ontario and Quebec, respectively. The sample statistics are summarized below.

Sample Size Percent in Favour Sample 1 from Ontario 400 62% Sample 2 from Quebec 400 60%

Let 1p be the proportion of people from Ontario in favour of the policy, and 2p be the proportion of people from Quebec in favour of the policy.

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(21) [2pts] To test if the proportion of people in support of the policy are equal among the two provinces, the test statistic is closest to

(A) 0.05 (B) 0.10 (C) 0.25 (D) 0.55 (E) 0.90 (22) [2pts] At 5% significance level , which one of the following is the best conclusion? (A) There is a significant difference between 1p and 2p . (B) There is no significant difference between 1p and 2p .

(C) There is a significant difference between 1p and

2p , where

1p and

2p are point

estimators of 1p and 2p , respectively.

(D) There is no significant difference between 1p and

2p , where

1p and

2p are point

estimators of 1p and 2p , respectively. (E) None of the above Questions (23) – (24): A telemarketing company wants to know if the sales (Y in thousand dollars) goes up as they make more number of phone calls (X) per day but spend less time per call. A simple regression model is assumed to predict Y from X. The following is the computer output from a random sample of 20 phone calls. Predictor Coeff StdDev Constant 1.2 0.5 X 0.3 0.2 (23) [2pts] To test if the simple regression model is significant, which one of the following is the value

of the test statistic ? (A) t=0.3 (B) t=2.4 (C) F=2.25 (D) F=5.76 (E) none of these

(24) [2pts] The correlation coefficient between X and Y is equal to

(A) 3

1 (B)

3

1 (C)

3

2 (D)

9

1 (E) none of these

REMEMBER, you must record your answers to the 24 multiple-choice questions on your BUBBLE FORM.

End of Final Exam

*Please detach this Attachment; It will NOT be graded* Attachment: Page 1 of 7 Table 1: Determinants of College Completion among High School Graduates: 1957, 1972, and 1992

Sources: Wisconsin Longitudinal Survey (WLS) 1957; National Longitudinal Survey (NLS) 1972; and National Educational Longitudinal Survey (NELS) 1988. Notes: The dependent variable is whether the high school senior received a four-year college degree (bachelor’s degree) within seven years (WLS, NLS) to eight years (NELS) of high school graduation. The mean of the dependent variable by sex is 0.143 for females and 0.217 for males in the 1957 class (WLS); is 0.257 for females and 0.297 for males for the 1972 class (NLS); and is 0.420 for females and 0.347 for males in the 1992 class (NELS). Math and reading achievement test scores and IQ scores are normalized into z-scores. High school rank percentile is a student’s percentile rank in their senior class. Courses are measured in terms of semesters in the WLS and NLS and by Carnegie units (full-time annual equivalents) in the NELS. Family background variables include log (family income), four race/ethnicity dummies, and four dummies for mother’s education. The race and ethnicity dummies are not available for the WLS. Missing data dummies are included for the three course variables, mother’s education, and family income. The regressions are linear probability models run by ordinary least squares. The regression samples are slightly smaller than the full samples for the descriptive tabulations in Appendix Tables 1, 2, and 3 because we delete observations with missing college-completion, test-score, or high-school-rank information from the regression samples. Standard errors are in parentheses.

*Please detach this Attachment; It will NOT be graded* Attachment: Page 2 of 7

Sample variance: = ∑ ( ) = ∑ − ∑( ) Sample s.d.: = √

Sample coefficient of variation: = Sample covariance: = ∑ ( )( ) = ∑ − ∑ ∑( )

Sample interquartile range: = 3 − 1 Sample coefficient of correlation: = = ∑

Addition rule: ( ) = ( ) + ( ) − ( ) Conditional probability: ( | ) = ( )( )

Complement rules: ( ) = ( ) = 1 − ( ) ( | ) = ( | ) = 1 − ( | ) Multiplication rule: ( ) = ( | ) ( ) = ( | ) ( ) Expected value: [ ] = = ∑ ( ) Variance: [ ] = [( − ) ] = = ∑ ( − ) ( )

Covariance: [ , ] = [( − )( − )] = = ∑ ∑ ( − )( − ) ( , ) Laws of expected value: Laws of variance: Laws of covariance: [ ] = [ ] = 0 [ , ] = 0 [ + ] = [ ] + [ + ] = [ ] [ + , + ] = ∗ [ , ] [ ] = [ ] [ ] = [ ] [ + + ] = + [ ] + [ ] [ + + ] = [ ] + [ ] + 2 ∗ [ , ] [ + + ] = [ ] + [ ] + 2 ∗ ( ) ∗ ( ) ∗ where = [ , ] Combinatorial formula: = !!( )! Binomial probability: ( ) = !!( )! (1 − ) for = 0,1,2, … , If is Binomial ( ~ ( , )) then [ ] = and [ ] = (1 − )

If is Uniform ( ~ [ , ]) then ( ) = and [ ] = and [ ] = ( ) Sampling distribution of : Sampling distribution of : Sampling distribution of ( − ): = [ ] = = = = − = − = [ ] = = = ( ) = − = ( ) + ( ) = [ ] = √ = = ( ) = − = ( ) + ( ) Sampling distribution of ( − ), independent samples: Sampling distribution of ( ), paired ( = − ): = [ − ] = − = [ ] = − = [ − ] = + = [ ] = = ∗ ∗ ∗ = [ − ] = + = [ ] = √ = ∗ ∗ ∗

*Please detach this Attachment; It will NOT be graded* Attachment: Page 3 of 7 Inference about a population proportion:

test statistic: = ( ) CI estimator: ± ⁄ ( ) Inference about comparing two population proportions:

test statistic under Null hypothesis of no difference: = ( ) ( ) Pooled proportion: =

CI estimator: ( − ) ± / ( ) + ( )

Inference about the population mean:

test statistic: = /√ CI estimator: ± / √ Degrees of freedom: = − 1

Inference about a comparing two population means, independent samples, unequal variances:

test statistic: = ( ) CI estimator: ( − ) ± ⁄ +

Degrees of freedom: =

Inference about a comparing two population means, independent samples, assuming equal variances:

test statistic: = ( ) CI estimator: ( − ) ± ⁄ + Degrees of freedom: = + − 2

Pooled variance: = ( ) ( )

Inference about a comparing two population means, paired data: ( is number of pairs and = − )

test statistic: = √⁄ CI estimator: ± ⁄ √ Degrees of freedom: = − 1

SIMPLE REGRESSION:

Model: = + + OLS line: = + = = = −

Coefficient of determination: = ( ) Residuals: = −

Standard deviation of residuals: = = ∑ ( ) Standard error of slope: . . ( ) = = ( )

*Please detach this Attachment; It will NOT be graded* Attachment: Page 4 of 7 Inference about the population slope:

test statistic: = . .( ) CI estimator: ± ⁄ . . ( ) Degrees of freedom: = − 2

Standard error of slope: . . ( ) = = ( )

Prediction interval for at given value of ( ):

± ⁄ 1 + + ( ) or ± ⁄ . . ( ) − + +

Degrees of freedom: = − 2 Confidence interval for predicted mean at given value of ( ):

± ⁄ + ( ) or ± ⁄ . . ( ) − + Degrees of freedom: = − 2

SIMPLE & MULTIPLE REGRESSION: Model: = + + +⋯+ + = ∑ ( − ) = + = ∑ ( − ) = ∑ = ∑ ( − ) = = = =

= = 1 − . = 1 − ( )⁄ ( )⁄ = −

Residuals: = − Standard deviation of residuals: = = ∑ ( )

Inference about the overall statistical significance of the regression model: = /( )/( ) = ( )//( ) = //( ) =

Numerator degrees of freedom: = Denominator degrees of freedom: = − − 1 Inference about the population slope for explanatory variable j:

test statistic: = CI estimator: ± / Degrees of freedom: = − − 1

Standard error of slope: . . = (for multiple regression, must be obtained from technology)

*Please detach this Attachment; It will NOT be graded* Attachment: Page 5 of 7

*Please detach this Attachment; It will NOT be graded* Attachment: Page 6 of 7

*Please detach this Attachment; It will NOT be graded* Attachment: Page 7 of 7