Econ375SampleMidterm

Econ375SampleMidterm - ECON 375 SAMPLE MIDTERM EXAM MAY 03...

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ECON 375 SAMPLE MIDTERM EXAM, MAY 03, SPRING 2010 Name ID 90 Minutes Instructions: 1. This is a closed book exam. 2. You are allowed to have a cheat sheet. 3. Please show all your work. 4. Fully label all graphs. Good Luck 1
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(1) (20 points) In a given population of two-earner male/female couples, male earnings have a mean $40 , 000 per year and a standard deviation of $12 , 000. Female earnings have a mean of $45 , 000 per year and a standard deviation of $18 , 000. The correlation between male and female earnings for a couple is 0 . 8. Let C denote the combined earnings for a randomly selected couple. a). What is the mean of C ? b). What is the covariance between male and female earnings? 2
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c). What is the standard deviation of C ? d). Convert your answers from dollars to euros. 3
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(2) (20 points) Consider the estimator tildewide Y = 1 n parenleftbigg 1 2 Y 1 + 3 2 Y 2 + 1 2 Y 3 + 3 2 Y 4 + ... + 1 2 Y n 1 + 3 2 Y n parenrightbigg Show that E ( tildewide Y ) = μ Y and V ar ( tildewide Y ) = 1 . 25 σ 2 Y /n . 4
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(3) (20 points) A regression of average weekly earnings on age measured in years using a random sample of college educated full time workers aged 25-65 yields the following: hatwider AWE = 696 . 7 + 9 . 6 × Age, R 2 = 0 . 023 , SER = 624 . 1 a) Explain what the coefficient values 696.7 and 9.6 mean.
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