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# exam1f2008 - ECON 303 EXAM 1 FALL 2008 DUE WEDNESDAY...

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ECON 303, EXAM 1 FALL 2008 DUE: WEDNESDAY, OCTOBER 8, 2008 at 12:40 PM Please show your work. There are 3 sections. Each section carries equal weight. If you have ANY questions, please ASK ME. Yes, the LC HONOR CODE APPLIES Section 1: Interpreting Information 1) A few years ago the news magazine The Economist listed some of the stranger explanations used in the past to predict presidential election outcomes. These included whether or not the hemlines of women’s skirts went up or down, stock market performances, baseball World Series wins by an American League team, etc. Thinking about this problem more seriously, you decide to analyze whether or not the presidential candidate for a certain party did better if his party controlled the house. Accordingly you collect data from 34 past presidential elections. You think of these data as comprising a population which you want to describe, rather than a sample from which you want to infer behavior of a larger population. You generate the accompanying table: Joint Distribution of Presidential Party Affiliation and Party Control of House of Representatives, 1860-1996 Democratic Control of House ( 0 Y = ) Republican Control of House ( 1 Y = ) Total Democratic President ( 0 X = ) 0.412 0.030 0.441 Republican President ( 1 X = ) 0.176 0.382 0.559 Total 0.588 0.412 1.00 (a) Interpret one of the joint probabilities and one of the marginal probabilities. (b) Compute ( ) E X . How does this differ from ( | 0) E X Y = ? Explain. . (c) If you picked one of the Republican presidents at random, what is the probability that during his term the Democrats had control of the House? (d) What would the joint distribution look like under independence? Check your results by calculating the two conditional distributions and compare these to the marginal distribution. 1

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2) Math SAT scores ( Y ) are normally distributed with a mean of 500 and a standard deviation of 100. An evening school advertises that it can improve students’ scores by roughly a third of a standard deviation, or 30 points, if they attend a course which runs over several weeks. (A similar claim is made for attending a verbal SAT course.) The statistician for a consumer protection agency suspects that the courses are not effective. She views the situation as follows: 0 : 500 Y H μ = vs. 1 : 530 Y H = . ()a Sketch the two distributions under the null hypothesis and the alternative hypothesis. ()b The consumer protection agency wants to evaluate this claim by sending 50 students to attend classes. One of the students becomes sick during the course and drops out. What is the distribution of the average score of the remaining 49 students under the null, and under the alternative hypothesis? ()c
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exam1f2008 - ECON 303 EXAM 1 FALL 2008 DUE WEDNESDAY...

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