# 02. ECON251 MT Sample Exam F2021.pdf - ECON251 SAMPLE...

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1ECON251SAMPLE MIDTERM EXAMCourse instructor:Asenka AsenovaName (as it appears in the Registrar):_____________________________________________________UMID:____________________________________________These are the instruction on the actual midterm exam. Please read them carefully, so that youdon’t need to invest time into this on the exam.InstructionsThis exam consists of 7 pages in total (page 8 is blank). Please, check the number of pages ofyour exam and contact the exam proctor if your exam has any missing pages.Show all your work on the exam sheet. If you need extra space you may use the last blank page.You will have80 minutesto complete the exam. The exam is worth180 pointsin total. Theweight of each question is reflected in its point count.The exam is closed book and closed notes:you are not allowed to use any textbooks, notes, orhomework, quizzes or sample exam solutions.Calculators are permitted; phones, laptops andother communication devices are not permitted.Sharing calculators is not permitted.A 1-page formula sheet is enclosed at the end of the exam.You may dis-attach the formulasheet for convenience. You do not need to submit it.Good luck!
2Note:On the actual midterm you will have space after each question to write down the answers,just like you did for the quizzes.Part I: Statistical inference (17 points in total)1.What does the Central Limit Theorem (CLT) state, and what is its importance in statistics? Beas precise as possible. (1 point)2.You are interested in estimating the average weekly hot dog consumption of all UM students.Suppose the population has meanµand varianceσ2.Assume you collect a random sample ofsizeN>3Comment on the properties of the following estimators of the population mean.A.The sample mean. Is it unbiased (show formally and explain what this means)? Is itefficient (yes/no and explain what this means)?(1 point)B.Another estimator𝝁𝝁=𝑿𝑿𝟏𝟏+𝟐𝟐𝑿𝑿𝟑𝟑. Is it unbiased (show formally)? Is it efficient (yes/noand explain why)? Also, find its variance.(1 point)C.Give an example of a biased estimator of the population mean in this context.Explain shortly what this means and show formally it is biased.(2 points)D.Give an example of an inconsistent estimator of the population mean in this context..𝟐𝟐

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Term
Winter
Professor
UtkuSuleymanoglu