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Examination Number:____________ Last Name______________First__________ Sign the Honor Pledge Below_____________ PID #________________________________ __________________________________ Write Your Section Number here:_________ University of North Carolina Economics 400: Economic Statistics Second Midterm Examination Prof. B. Turchi April 5, 2018 General Instructions: Answer all 3 questions (with multiple parts) on this examination, writing your answers on the exam paper itself. Tear off and use the scratch page on the back of the exam for extra work but put all relevant calculations on the test paper. Sign the Honor Pledge above. Express all answers to a precision of at least 3 decimal points. Show your work to be eligible for partial credit. Be sure to note that tables and formulas are on pages 7-10 of the exam. Part I: The UPS® Team Performance Index for basketball is a proprietary data index that measures offensive and defensive efficiency for all 343 NCAA Division I men's and women's basketball teams for the 2017-2018 regular season. It is designed to identify well-balanced teams that do multiple things well, similar to how UPS excels in logistics. (Obligatory commercial, since I'm ripping off their index.) The Team Performance Index (TPI) includes six key statistical components that are combined in a manner that rewards teams for performing efficiently and effectively in all categories to create the Index, ranking them from highest to lowest. The TPI can take on values well over 100 (high) to zero (lowest) 1. I have randomly sampled (without replacement) 25 of the schools that have both men's and women's teams. +------------------------------------------------------------+ | Team indexdiff MIndex WIndex | |------------------------------------------------------------| 1. | Siena Saints 20.48 97.77 77.29 | 2. | Alcorn State Braves 16.28 84.13 67.85 | (a) (6 points) Compute the sample mean of 3. | Kentucky Wildcats -4.03 121.25 125.28 | 4. | Arkansas State Red Wolves -11.73 99.83 111.56 | the Men's TPI (Mindex) and the standard 5. | Michigan Wolverines 9.86 119.53 109.67 | |------------------------------------------------------------| error of the mean. 6. | Rhode Island Rams 20.03 98.87 78.84 | 7. | Cleveland State Vikings 21.71 108.7 86.99 | 8. | Air Force Falcons 32.19 92.41 60.22 | 9. | Purdue Boilermakers -21.23 99.43 120.66 | 10. | Missouri Tigers -.19 110.96 111.15 | |------------------------------------------------------------| 25 11. | North Dakota -13.39 92.65 106.04 | 12. | Pittsburgh Panthers 26.32 119.84 93.52 | MIndex 13. | Kent State Golden Flashes 16.85 97.91 81.06 | i 14. | VCU Rams 8.47 115.35 106.88 | i1 15. | Valparaiso Crusaders 23.76 101.63 77.87 | x 101.838 |------------------------------------------------------------| 16. | Bethune-Cookman Wildcats -5.72 75.56 81.28 | 25 17. | American University Eagles -6.84 108.29 115.13 | 18. | Pepperdine Waves 15.97 97.37 81.4 | 19. | Florida Atlantic Owls 3.06 93.34 90.28 | n 20. | UNI Panthers 1.38 104.7 103.32 | x x 2 |------------------------------------------------------------| i 21. | Cal Poly Mustangs -8.83 95.71 104.54 | i1 22. | Gardner-Webb Runnin' Bulldogs 6.96 99.13 92.17 | s n 1 11.77926 23. | New Mexico Lobos 30.27 122.96 92.69 | sx 2.356 24. | Western Illinois Leathernecks .78 90.51 89.73 | n n 5 25. | Houston Cougars 23.48 98.12 74.64 | +------------------------------------------------------------+ Mtm2S18.lwp Page 1 of 11 Examination Number:____________ (b) (6 points) The quantitative-normal plot of the women's TPI is as shown below. Can we assume that this sample of women's scores is drawn from a normal population? Why/Why not? Qnorm Plot of Women's TPI 65.44702 93.6024 121.7578 Yes, the sample points follow the 45-degree line pretty closely. 140 120 120.66 100 Women's TPI 92.17 80 67.85 60 60 80 1 00 120 Inverse Normal Grid lines are 5, 10, 25, 50, 75, 90, and 95 percentiles (c) (16 points) Do schools that produce high quality men's teams also produce high quality women's teams, and vice versa? Use the data in the table to test the hypothesis that schools produce teams of equal quality versus that alternative that they don't. Explain your hypotheses and assumptions and show your work. Use a significance level alpha= 0.01 We want to test the hypothesis that indexdiff = 0 against the alternative that it is not equal to zero: H0 : indexdiff 0 Ha : indexdiff 0 We assume a normally distributed population based on (b) above. Compute the mean of indexdiff which equals 8.2356 (men minus women) n 2 xi x i1 s 14.90528 Compute s n 1 2.981 x n n 5 x 0 8.2356 t 2.763 Compute t-score: sx 2.981055 0.01 0.005 2.797 Critical value for df = 24 is: 2 2 We cannot reject the null hypothesis that the mean difference between men’s and women’s teams is zero. Mtm2S18.lwp Page 2 of 11 Examination Number:____________ d) (16 points) Another way of asking the question in part c) above is, “Does the quality of the men’s basketball team at a college predict the quality of the women’s team at the same college?” Below find the results of a regression of Women’s TPI on Men’s TPI from the table above: regress WIndex MIndex Source | SS df MS Number of obs = 25 -------------+---------------------------------- F(1, 23) = XXXX Model | 1899.46654 1 1899.46654 Prob > F = 0.0077 Residual | 5132.54312 23 223.154049 R-squared = XXXXXX -------------+---------------------------------- Adj R-squared = Total | 7032.00966 24 293.000402 Root MSE = 14.938 ------------------------------------------------------------------------------ WIndex | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- MIndex | .7552529 .2588683 XXXX XXXXX .2197429 1.290763 _cons | 16.68896 26.53139 0.63 0.536 -38.1954 71.57332 ------------------------------------------------------------------------------ (i) What is the F-Statistic for this regression?_________________ (ii) What is the t-statistic for the slope coefficient?______________ (iii) What is the p-value for the slope coefficient? _______________ (iv) What is the R2 for the regression?_________________________ (v) What is the correlation between MIndex and Windex?_________ (vi) Draw a causal diagram in the box below showing the relationship between MIndex and Windex (include error term). Do variations in Mindex cause significant variations in Windex? Why? Could the causation run the other way?_______________________________________________________ ___________________________________________________________ . regress WIndex MIndex Source | SS df MS Number of obs = 25 -------------+---------------------------------- F(1, 23) = 8.51 Model | 1899.46654 1 1899.46654 Prob > F = 0.0077 Residual | 5132.54312 23 223.154049 R-squared = 0.2701 -------------+---------------------------------- Adj R-squared = 0.2384 Total | 7032.00966 24 293.000402 Root MSE = 14.938 ------------------------------------------------------------------------------ WIndex | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- MIndex | .7552529 .2588683 2.92 0.008 .2197429 1.290763 _cons | 16.68896 26.53139 0.63 0.536 -38.1954 71.57332 ------------------------------------------------------------------------------ Mtm2S18.lwp Page 3 of 11 Examination Number:____________ 1899.46654 F-statistic 8.512. 223.154049 .7552529 t-statistic = 2.92 .2588683 p-value for slope coefficient is 0.0077 or rounded to 0.008 1899.46654 R-square = 0.2701 7032.00966 Correlation between MIndex & WIndex is: R2 0.5197 WIndex MIndex Yes, the variations in Mindex appear to have a significant positive effect on variations in Windex. The slope coefficient is positive (1899.46654) and significantly different from zero. However, the causations could run the other way: variations in the women’s teams’ quality could be having a positive effect on the men’s teams. 2. One of the six measures of a team's TPI is an index called the "ball-handling index" (BH). This index includes assists/game, steals/game, opponent assists/game, opponent steals/game. Below, the table shows BH indexes of 13 men's teams and 16 women's teams randomly sampled independently from the populations of Division I teams. +------------------------------------------------+ | Team BH sex | |------------------------------------------------| (a) (14 points) One measure of 1. | North Carolina Central Eagles 84.7 Women | 2. | North Dakota 95.05 Women | ball-handling skill differentials 3. | Creighton Bluejays 100.25 Women | 4. | Fairfield Stags 98.77 Women | between men and women would be 5. | San Diego Toreros 111.96 Women | |------------------------------------------------| 6. | Chicago State Cougars 79.54 Women | the hypothesis that the ball handling 7. | Long Beach State 49ers 100.35 Women | skills of women players in the 8. | Liberty Flames 94.98 Women | 9. | Evansville Aces 99.35 Women | population of college players vary 10. | Lafayette Leopards 96.45 Women | |------------------------------------------------| more widely than do the 11. | Memphis Tigers 101.33 Women | 12. | Wyoming Cowboys 108.72 Women | ball-handling skills of men players. 13. | Louisiana-Monroe Warhawks 92.64 Women | 14. | North Carolina State Wolfpack 107.08 Women | 15. | SMU Mustangs 98.25 Women | Set up and test the hypothesis that |------------------------------------------------| 16. | Fresno State Bulldogs 109.95 Women | the variability of ball handling 17. | Marist Red Foxes 95.56 Men | 18. | UTSA Roadrunners
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