1 Dr. Valerie R. Bencivenga Economics 329 Feb. 16, 2017 MIDTERM EXAM #1 Instructions: Answer the questions below in a blue exam book. There are 9 questions worth 220 points. This is a closed book exam. You may use a calculator (no device with wireless). The formula sheet is at the end. Show your work to receive credit. The exam will last two hours. Good luck! (20 points) 1. Starting with a variable X, create the linear transformation Y a bX. Assume X0 and b0. For each of the graphs below, say what you can infer about “b”: - 0 < b < 1 - b = 1 - b > 1 Also, say what you can infer about “a”: - a < 0 - a = 0 - a > 0 - a could be negative, zero, or positive No explanations are needed. Part a: Part b: Part c: Part d: NAME: ___________________________________ EID: ______________ You must return the exam questions along with your blue exam book, or you will get a zero on the exam. Only your blue exam book will be graded. X X2 (35 points) 2. In this question, you do NOT need to evaluate your numerical answers. Full credit will be given for the correct expression that you WOULD evaluate. A large water park hires you to forecast the number of customers each month for the next calendar year. In Eco 341K you’ll learn how to forecast. Here, we’ll discuss the data set. You decide to work with the following variables. For each variable, you have many years of monthly data. A = attendance at the water park (number of customers) P = price of admission to the water park (in 2015 dollars) R = number of water rides at the park (on the first day of the month) W = number of days during the month when it rained during business hours T = average daily high temperature G = price per gallon of gasoline (in 2015 dollars) N = surrounding population (population within 100 miles of the park) C = 1 if the economy is in a contraction (recession), 0 if not S = 1 if the month is a summer month, 0 if not sample means sample variances and standard deviations sample covariance A 18,000 2AAs 9, 000,000 s 3,000   ANs 48,000,000 N 2,000,000 2NNs 400, 000, 000 s 20, 000   a. Say whether each of the nine variables in the data set is continuous, approximately continuous, or discrete (and if it is discrete, whether or not it is a dummy variable). No explanations are required. (9 points) b. The water park lets the first 50 children in free each day (the first 50 don’t pay). This means 1,500 per month don’t pay. You decide to create the variable X = thousands of paying customers. Write X as a linear transformation of A. Assume every month has 30 days. (3 points) c. Give expressions for the sample mean of X and the sample variance of X. (4 points) d. You decide to change the units of the surrounding population to millions of people. Use Y to denote surrounding population in millions. State Y as a linear transformation of N. (3 points) e. Give expressions for the sample mean of Y and the sample variance of Y. (4 points) f. What are the units of the covariance between A and N? What are the units of the covariance between X and Y? Give an expression for the covariance between X and Y. (6 points) g. Give an expression for the correlation between A and N. Without doing any calculations, give an expression for the correlation between X and Y. (4 points) h. C 0.2. Explain in words what this value of the sample mean of C tells you. (Don’t make this too hard.) (2 points)3 (35 points) 3. Comparing 2016 to 2015, every person living in the United States was a nonmover (didn’t change where they live), moved within the United States, or moved to abroad. Below is a table giving the relative frequency distribution (“rel freq”) and cumulative relative frequency distribution (“cumulative”) by age category, for each of these three subsets of people, in percentage points. The table covers everyone living in the US in 2015 who was at least one year old. Source: U.S. Census Bureau, Current Population Survey, 2016 Annual Social and Economic Supplement. Nonmover Within US Abroad AGE Rel freq Cumulative Rel freq Cumulative Rel freq Cumulative 1 to < 10 11.08 11.08 15.77 15.77 14.35 14.35 10 to < 20 13.29 24.37 12.23 27.99 11.23 25.59 20 to < 30 12.13 36.50 29.62 57.62 32.92 58.50 30 to < 40 12.76 49.27 16.88 74.50 21.76 80.27 40 to < 50 13.10 62.37 10.27 84.77 11.39 91.65 50 to < 60 14.65 77.02 7.85 92.62 5.15 96.80 60 to < 70 12.23 89.25 4.62 97.24 2.11 98.91 70 to < 80 6.88 96.13 1.71 98.95 0.94 99.84 80+ 3.87 100.00 1.05 100.00 0.16 100.00 100.00 100.00 100.00 a. For each subset of people (nonmovers, within US, abroad), give the age category in which the third quartile falls. Explain for one of them (not all three). Do NOT calculate the third quartiles. (8 points) b. Calculate the median ages of nonmover, people who move within the US, and people who move to abroad. Keep two decimals. (12 points) c. What assumption is your calculations in part b based on? (5 points) d. If we wanted to compare the ages of people who are nonmovers, move within the US, and move to abroad, what do your answers to parts a and b suggest? Explain your thinking in 2 or 3 sentences. (5 points) e. Which measure of central tendency would you use when describing these relative frequency distributions? Briefly explain. You must explain to receive credit. (5 points) f. (EXTRA CREDIT – 5 POINTS) Is the moving decision (nonmover, within, abroad) independent of the age category? Explain why or why not. You must explain to receive credit.4 (20 points) 4. The data in this question are related to the data in the previous question. Here, we have six categories of educational attainment (row labels). The table reports relative frequencies in percentage points. Interpret these relative frequencies as probabilities. (The first row contains people who are 24 years or older who do not have at least a high school degree. People who are under 24 years old and who don’t have at least a high school degree are in the last row.) EDUCATIONAL ATTAINMENT Nonmover Within US Abroad Not a high school graduate 6.74 0.68 0.02 7.45 High school graduate 17.95 1.69 0.04 19.68 Some college or AA degree 16.59 1.68 0.03 18.30 Bachelor's degree 12.77 1.37 0.08 14.22 Prof. or graduate degree 7.77 0.77 0.06 8.61 Persons aged 1