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Midterm

MidtermExamSectionC_solutions.pdf

7 Pages
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Department
Economics
Course Code
ECON 3210
Professor
Razvan Sufana

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Department of Economics York University AP/ECON 3210 Section C Use of Economic Data Prof. Razvan Sufana Midterm Exam Last Name: ________________________________ First Name: ________________________________ Student Number: ________________________________ Instructions: • Print your last name, first name, and student number in the space above. • The duration of this exam is 2 hours. • You are required to answer all questions. • Total marks: 100. • You can use pen or pencil (random tests will be photocopied). • Show all your work in questions 2 and 3. • Only simple calculators are allowed (no programmable calculators). • Use four decimal places in your answers. • Statistical tables are attached. _____________________________________________________________ Do not write in the space below. Question Marks 1 ____ 2 ____ 3 ____ Total ____ 1. [25 marks] Indicate whether each of the following statements is TRUE, FALSE, or UNCERTAIN. Circle only one answer below each statement. 1. a) [5 marks] An interval estimate of the slope parameter, based on one sample of data, includes the true value of the slope if the sample size is sufficiently large. TRUE FALSE UNCERTAIN 1. b) [5 marks] The level of significance of a test is equal to the probability of a Type I error. TRUE FALSE UNCERTAIN 1. c) [5 marks] In the simple linear regression model, a 95% confidence interval for a regression parameter is narrower than a 90% confidence interval for the same parameter, if the two intervals are constructed based on the same sample of data. TRUE FALSE UNCERTAIN 1. d) [5 marks] If any of the first five assumptions of the simple linear regression model is not true, the Gauss-Markov Theorem does not hold. TRUE FALSE UNCERTAIN 1. e) [5 marks] The larger the variance of the error term, the larger the precision of the least squares estimators. TRUE FALSE UNCERTAIN 2 2. [37 marks] Suppose that1Y, 2 i3 a random sample from a N(μ,σ )2 population. Consider the following estimators of the population mean: ~ 1 1 1 1 1 1 Y = Y1+ Y 2 Y3and Y = Y 1 Y2+ Y 3 4 4 2 3 3 3 ~ 2. a) [9 marks] Show that and Y are linear and unbiased estimators of the population mean. Answer: Y and Y are linear estimators since each estimator can be written as  aiYi, whereai are constants for i = 1, 2, 3. E(Y) = 1 E(Y ) + 1E(Y ) + 1 E(Y ) = 1μ + 1μ + 1 μ = μ 4 1 4 2 2 3 4 4 2 E(Y) = 1 E(Y ) +1 E(Y ) + 1E(Y ) = 1 μ +1 μ +1 μ = μ 3 1 3 2 3 3 3 3 3 ~ 2. b) [6 marks] Find the variances of YYa.d Answer: 1 1 1 1 1 1 3 var(Y) = var(Y1)+ var(Y2)+ var(Y3)= σ + σ + σ = σ 2 16 16 4 16 16 4 8 2 1 1 1 1 2 1 2 1 2 σ var(Y) = var(Y1)+ var(Y2)+ var(Y3)= σ + σ + σ = 9 9 9 9 9 9 3 3 ~ 2. c) [6 marks] Explain briefly which one of the two estimators (Y you would prefer. Answer: ~ From 2. a) , Y andY are unbiased. 2 From 2. b),var(Y)= 3 σ , var(Y) =σ . 8 3 Since var(Y)
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