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Unformatted text preview: Solutions for Statistics 101 Midterm Professors Abraham Wyner & Alexander Rakhlin Solutions prepared by Adam Kapelner and Emil Pitkin 100 points total 1 [3 pts] The average crowd size in the 50 games is e 2 [3 pts] The distribution of Crowd Size is a 3 [3 pts] The Empirical Rule would tell us that for 2/3 of of the 50 games the crowd size is between a 4 [3 pts] The Inter Quartile Range for the NumSold is a 1 5 [3 pts] Judging from the information above d 6 [3 pts] On average, each extra person is expected to purchase about c since r s y s x = . 488 7 [4 pts] Given the information above, calculate the equation of the regression line. Answer: y = r s y s x x + y r s y s x x y = . 488 x . 763 8 [3 pts] If 16 thousand people attend the game, the model predicts that the vendor will sell on average how many hot dogs? Answer: 7.05 thousand (7,050) hotdogs, because 488 * 16 . 763 = 7 . 05 2 9 [4 pts] If you only knew that 7000 hot dogs were sold at a game, how big do you think the crowd was on that day? Answer: 16.46 thousand (16,460) people. We regress attendance on num ber of hot dogs sold: x = r s x s y y + x r s x s y y x = 1 . 665 y + . 4803 16 . 46 = 1 . 665 * 7 + . 4803 10 [5 pts] In one game, attended by 20 thousand people, 10 thousand hot dogs were sold. Is this amount fairly typical or unusual? Explain. Answer: This is an unusual amount, far exceeding the expected number of hot dogs sold. At a game attended by 20 thousand people, the expected number of hot dogs sold is 9,000: y = . 488 * 20 . 763 = 9 . 00, which is one thousand less than the number actually sold. Since the standard deviation of the residuals is RMSE = s y * 1 r 2 = . 523 the given game represents a departure of almost 2 standard deviations from a typical game. 11 [3 pts] Suppose you choose a game at random from one of the 50 games in the data set. Let X= numsold (in thousands) and Y=crowd size (in thousands). Calculate the Cov(X,Y). 3 Answer: 2.43 Cov [ X,Y ] = xy * s x * s y = . 9015 * 2 . 23 * 1 . 21 = 2 . 43 The baseball World Series between NY Yankees and the Phillies will al ternate its location between NY and Philadelphia. The first 2 games will be played in NY, followed by 3 games in Philadelphia, followed by 2 games in NY. Although the schedule allows for 7 games, the series will terminate as soon as one team wins four games. Thus, the actual series are is not likely to be a full 7 games. Let N be the random variable equal to the number of games played. As sume that P(N=7) = .07, P(N=6) = .28 and P(N=5) = .25. Let X be the number of games played at Yankee stadium in the Bronx (NY) and let Y be the number of games played at Citizens Bank Park, Philadel phia....
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This note was uploaded on 04/04/2012 for the course STAT 101 taught by Professor Heller during the Fall '08 term at UPenn.
 Fall '08
 Heller
 Statistics

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