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statsexam3f09

statsexam3f09 - Economic Statistics Exam 3 Last name First...

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Economic Statistics Exam 3 Last name: December 14, 2009 First name: PID: Please sign that you abide by the honor pledge: This exam contains twenty short answer questions (worth 6 points each) and three long answer questions (worth 15 points each). In all problems where you need to make a calculation, simplify your answer as much as possible. Show your work clearly to be eligible for partial credit. Some PDFs: Some probabilities: f ( x ) = 1 2 πσ 2 e ( X μ ) 2 σ 2 P [ x a ] = 1 e λ a f ( x ) = 1 u P [ x ] = λ x e λ x ! f ( x ) = λ e λ x P [ x ] = n ! x !( n x )! p x (1 p ) n x 1. Suppose that the random variable X is drawn from a normal distribution with a mean of 12 and a variance of 16. What is the probability that X is between 10 and 18? 2. A researcher draws a random sample of size N = 9 from a normal distribution. His sample has a mean of 52 and a standard deviation of 6. Construct a 95% confidence interval for the population mean.

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Econ 400 Midterm 3, page 2 of 9. 3. Suppose that you estimate Y as a quadratic function of X : Y i = β 0 + β 1 X i + β 2 X i 2 + e i . In Stata, you type: . gen x2 = x^2 . reg y x x2 Source | SS df MS Number of obs = 1000 ---------+------------------------------ F( 2, 997) = 233.17 Model | 48166.9162 2 24083.4581 Prob > F = 0.0000 Residual | 102975.057 997 103.284912 R-squared = 0.3187 ---------+------------------------------ Adj R-squared = 0.3173 Total | 151141.973 999 151.293267 Root MSE = 10.163 -------------------------------------------------------------------------- y | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+---------------------------------------------------------------- x | -1.570586 .3091338 -5.08 0.000 -2.177213 -.9639583 x2 | 4.546693 .2165667 20.99 0.000 4.121714 4.971671 _cons | 1.91043 .397595 4.80 0.000 1.130211 2.690649 -------------------------------------------------------------------------- What is the estimated marginal effect of X on Y (that is, Y X )? 4. In the previous question, how would you test the hypothesis that X has no effect at all on Y ? Either write out your null and alternative hypotheses, or write the Stata command(s) you would use to test it. 5. I have an egg carton with 12 eggs; 4 are fresh, and 8 are rotten. If I select three eggs at random from the carton, what is the chance that all three are rotten?
Econ 400 Midterm 3, page 3 of 9.

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