Econ 210 Winter 2008 Practice Questions Midterm II - Solutions_1

Econ 210 Winter 2008 Practice Questions Midterm II - Solutions_1

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Solutions 1. True/False (Don’t forget an explanation) a) Chi-square random variables can be negative. FALSE. A Chi-square random variable is the sum of independent, squared standard normal variables and thus cannot be negative. b) The mean of a Chi-square random variable with N degrees of freedom is N. TRUE. ( 29 ( 29 ( 29 2 2 2 2 2 2 1 2 3 i ....... since E x 1 N N E E z z z z N χ = + + + + = = c) You calculate a sample mean of 68. This is a random variable. FALSE. It is an estimate and as such not a random variable. d) 1 2 3 4 2 x x x x X + + + = is a linear estimator. TRUE. It fits the general scheme of the general linear estimator discussed in class. e) Unbiasedness is a large sample property of an estimator. FALSE. Bias/Unbiasedness is not tied to any sample size. f) The sample mean is the most efficient estimator among linear unbiased estimators TRUE. It is the Best (most efficient) Linear Unbiased estimator. g) A researcher draws a random sample of individuals from a population and then records their wages every year. The resulting wage sample is i.i.d. FALSE. While the different years themselves represent an i.i.d. sample the fact that the wages of a person in different years are not independent leads to a non- i.i.d sample. h) Every random sample is also an i.i.d sample FALSE. See b) i) The law of large numbers states that the samples mean will be normally distributed in large samples FALSE. The CLT states that. j)
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This note was uploaded on 09/25/2010 for the course ECON 210 taught by Professor Pavan during the Winter '09 term at Northwestern.

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Econ 210 Winter 2008 Practice Questions Midterm II - Solutions_1

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