# UT ECO 329 - STAT S2017 MT#1 q BLUE (6 pages)

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## STAT S2017 MT#1 q BLUE

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- Pages:
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- School:
- University of Texas at Austin
- Course:
- Eco 329 - Economic Statistics

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NAME EID Dr Valerie R Bencivenga Economics 329 Feb 16 2017 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 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 X 0 and b 0 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 1 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 s2A 9 000 000 s A 3 000 sAN 48 000 000 N 2 000 000 2 sN 400 000 000 sN 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 2 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 AGE 1 to 10 10 to 20 20 to 30 30 to 40 40 to 50 50 to 60 60 to 70 70 to 80 80 Nonmover Rel freq Cumulative 11 08 11 08 13 29 24 37 12 13 36 50 12 76 49 27 13 10 62 37 14 65 77 02 12 23 89 25 6 88 96 13 3 87 100 00 100 00 Within US Rel freq Cumulative 15 77 15 77 12 23 27 99 29 62 57 62 16 88 74 50 10 27 84 77 7 85 92 62 4 62 97 24 1 71 98 95 1 05 100 00 100 00 Abroad Rel freq Cumulative 14 35 14 35 11 23 25 59 32 92 58 50 21 76 80 27 11 39 91 65 5 15 96 80 2 11 98 91 0 94 99 84 0 16 100 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 3 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 Not a high school graduate High school graduate Some college or AA degree Bachelor s degree Prof or graduate degree Persons aged 1 to 24 Nonmover 6 74 17 95 16 59 12 77 7 77 27 02 88 84 Within US 0 68 1 69 1 68 1 37 0 77 4 56 10 75 Abroad 0 02 0 04 0 03 0 08 …

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