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statsexam2s09sol

# statsexam2s09sol - Economic Statistics Exam 2 Last name...

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Economic Statistics Exam 2 Last name: March 31, 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. Some PDFs: Some probabilities: f ( x ) = 1 2 !" 2 e # ( X # μ ) 2 " 2 P [ x ! a ] = e " # a f ( x ) = 1 u ! ! P [ X ] = μ x e ! μ X ! f ( x ) = ! e " ! x P [ X ] = N ! X !( N ! X )! p X (1 ! p ) N ! X Short Questions ( 6 points apiece ) 1. The formal statement of a hypothesis has two parts. What are these called, and what does each describe? The “null hypothesis” is the idea that we wish to test; the “alternative hypothesis” is a formal statement of what we assume to be true if the null is false. 2. What is the formula for the minimum variance unbiased estimator of the population variance? s x 2 = 1 ( N ! 1) ( X i ! X ) 2 i = 1 N "

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Econ 400 Midterm 2, page 2 of 7. 3. Each person has a 10% chance of being left - handed. I have a class of 100 students, and my classroom has 15 left - handed desks. What is the chance that I have more left - handed students than desks? This uses the normal approximation to the binomial distribution. The number of lefties is distributed approximately X ~ N ( Np , Np (1 ! p )) = N (10,9) . For a normal distribution with mean of 10 and standard deviation of 3 = 9 , P [ X > 15] = P [ Z > (15 ! 10) / 3] = 0.0478 . 4. You want to determine whether the earnings of former prison inmates differ significantly from the earnings of the rest of the population. Construct an 80% confidence interval for the difference in earnings between these groups: | Summary of earnings inmate | Mean Std. Dev. Freq.
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