statsexam1s09 sol

statsexam1s09 sol - Economic Statistics Exam 1 Last name...

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Economic Statistics Exam 1 Last name: February 17, 2009 First name: PPID: Section number: Please sign that you abide by the honor pledge: This exam contains fifteen short answer questions ( worth 6 points each ) and three long answer questions ( worth 15 points each ) . Show your work clearly to be eligible for partial credit. In all problems where you need to make a calculation, simplify your answer as much as convenient. In questions with multiple parts, you should respond as if your answers to previous parts were correct. Formulas: P [ X ] = N ! X !( N ! X )! p X (1 ! p ) N ! X P [ X ] = e ! μ X X ! Short Questions ( 6 points apiece ) 1. Suppose that overall, 20% of people have blond hair, and 25% of people have blue eyes, but 60% of the population has neither blond hair nor blue eyes. Are these two events independent? ( Explain. ) The events are independent if P ["not blond" and "not blue"] = P ["not blond"] ! P ["not blue"] . In this problem, P ["not blond"] ! P ["not blue"] = ! P ["blond"]) " ! P ["blue"]) = ! 0.20) " ! 0.25) = (0.80) ! (0.75) = 0.60 . Since this is the same as P ["not blond" and "not blue"] , the events are independent. 2. In the previous problem, what is the probability that a person has blond hair or blue eyes ( or both ) ? One solution technique: the “complement” of being “blond, blue - eyed, or both” is “neither blond nor blue - eyed”. The probability of this event is 1 ! 0.60 = 0.40 . 3. How do we determine the length of the whiskers in a box - and - whisker plot? The whiskers could extend as far as 1.5 ! ( IQR ) from the 25th and 75th percentiles, though they actually end at the nearest datapoint within this interval.
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Econ 400 Midterm 1, page 2 of 7. 4. According to the National Weather Service, Chapel Hill has 2.7 snowy days per year, on average. What is the probability that we have three or more? This should be modeled using the Poisson distribution: P [ X ] = e ! 2.7 2.7 X X ! . P [ X > 3] = 1 ! P [ X " 2] = 1 ! ( P [0] + P [1] + P [2]) . Evaluate these for the Poisson distribution.
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statsexam1s09 sol - Economic Statistics Exam 1 Last name...

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