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:Temple University
Department of Economics
Economics 615Econometrics I
Midterm Exam
Fall 2005
Directions: You have 2 hours and 20 minutes to complete this exam. You must show your work. Your work must be your own; you may neither give nor receive help. This is a closed book exam. You may not use your cell phone for any purpose during the exam.
A truth serum has the property that 90% of the guilty suspects are properly judged while, of course, 10% of guilty suspects are improperly found innocent. On the other hand, innocent suspects are misjudged 1% of the time. If the suspect was selected from a group of suspects of which only 5% have ever committed a crime, and the serum indicates that he is guilty, what is the probability that he is innocent?
A company produces blends of tobacco with each blend containing various proportions of Turkish (t), domestic (d) tobaccos, and other tobaccos. The proportion of Turkish and domestic in a blend are random variables with joint density function EMBED Equation.3 (a) Find the probability that in a given box the Turkish tobacco accounts for over half the blend.(b) Find the probability that the proportion of Turkish tobacco is less than 1/8 if it is known that the blend contains domestic tobacco.
According to a study published by a group of sociologists at the University of Massachusetts, approximately 49% of the Valium users in the state of Massachusetts are white-collar workers. What is the probability that between 482 and 510, inclusive, of the next 1,000 randomly selected Valium users from this state would be white-collar workers?
A recent research report reports that mice with an average life span of 32 months will live to be about 40 months old when 40% of the calories in their food are replaced by vitamins and protein. Is there any reason to believe that < 40 if 25 mice that are placed on this diet have an average life of 38 months with a sample standard deviation of 5.8 months? Clearly state any, and all, assumptions that you make in your answer.
A random sample of 12 economics students was given a pre-test on their knowledge of economics. They then took principles of economics. In addition to recording their grade the instructor also kept track of the number of class meetings that each student missed. A research assistant was given the task of determining estimates of the coefficients in the regression model EMBED Equation.3 Unfortunately the R.A. didnt have time to complete the task. From the following information on the data cross products calculate the regression coefficients.
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6. Briefly explain the motivation and interpretation of the Wald, Likelihood Ratio and Lagrange multiplier test statistics. A graph might help.
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