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Unformatted text preview: Solutions to Midterm Fall 2006 1. (8 pts.) Assume you know that in a particular industry the mean wage equals $12 per hour. You also know that 16% of the workforce in this sector is unionized and that the mean wage for non-unionized labor equals $10 per hour. Find the hourly wage of union members in this industry. E(w) = E(w|union)*P(union) + E(w|non-union)*P(non-union) $12 = E(w|union)*0.16 + $10*0.84 => Solve this for E(w|union)= $22.5 2. Answer the following questions. a) (4 pts.) Describe the importance of the Central Limit Theorem. Consider a sample of N i.i.d random variables with E(Y)= Y μ and V(X)= 2 Y σ (variance finite). The CLT states that - N Y Y Y 2 σ μ will follow a standard normal distribution when the sample size gets very large. The importance of this result lies in the fact that we have to know very little about underlying distribution of Y while still being able to perform inference using the standard normal table. Put differently, without the CLT we could run regressions but would not be able to perform any reliable statistical tests on the estimated coefficients. b) (4 pts.) Assume you draw an i.i.d sample (N=256) from X~(3,16). What is the probability that the sample mean is smaller than 3.3? With a sample size of 256 we can invoke the CLT, use the standard normal distribution, and approximate X~N(3,16/256). Construct the z-value 2 . 1 4 * 3 . 3 3 . 3 256 16 = =- . P(z<1.2)=.8849 c) (4 pts.) How big of a sample would you need that the sample mean is within 1% of its true value ( % 1 ± μ ) with a probability of at least 99%?...
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This test prep was uploaded on 04/07/2008 for the course ECON 281 taught by Professor Habermalz during the Spring '08 term at Northwestern.
- Spring '08