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-----------------------------------------------------------------------------------------------------------ERASMUS UNIVERSITY ROTTERDAM ERASMUS SCHOOL OF ECONOMICS DEPARTMENT OF ECONOMETRICS -----------------------------------------------------------------------------------------------------------APPLIED STATISTICS - FEB11005X Assignment 2 Tutorial group: Bonus group name: -------------------------------------------------------------------------------------------Student 1: Name................................ Exam nr: Signature............................................ Student 2: Name................................ Exam nr: Signature........................................... Student 3: Name................................ Exam nr: Signature........................................... Student 4: Name................................ Exam nr: Signature........................................... 1 Note: Always explain how you arrived at our answers! No credit is given to answers without proper motivation. Exercise 1 The ages of a sample of 11 salespersons are summarized in the stem-and-leaf plot below: STEM 2 3 4 5 1) 2) LEAF 1 279 13478 36 The median age of the salespersons in this sample is 43 years. True The mean age is smaller than the median age. TRUE, sum of all ages / n 2 Exercise 2 It is known that the scores for an admission exam for a certain MBA program are normally distributed. For an admission exam, 24.20% receives less than 130 points and 75.80% receives less than 270 points. 3) The mean score for an admission exam is 200 points. True (p=0.242, z=-0.7; p=0.758, z=0.7) Mean must be in between: 200 4) The standard deviation for the scores equals, rounded to whole points, 100 points. True 3 Exercise 3 Anthony thinks that for a certain statistics course, the grade for the preceding mathematics course can be used to predict the grade in statistics. Based on data of the previous year, the least-squares regression equation summarizing this relationship is: s = 3 + 0.7m (where s is the statistics grade and m the mathematics grade). It is also known that last year’s mean grade for statistics was 6.5 and the standard deviation for the statistics’ grades was twice as large as that of the mathematics grades. 5) This year, Anthony scored a 10 for his mathematics course. Using his regression equation, he predicts that his statistics grade will be lower than his mathematics grade. False, should be 3+0.7*10=10 6) Last year, the mean grade for mathematics was larger than the mean grade for statistics. Incorrect, see formula 4 7) The correlation coefficient between the mathematics and statistics grades was 0.35 True, because of the standard deviation being twice as big. 0.7=r*2/1, r=0.35 Exercise 4 The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month’s sales (in $1,000s) and the years of experience of 10 randomly selected salespeople working for this store. These data are listed below. Salesperson 1 2 3 4 5 6 7 8 9 10 Years of Experience (x) 0 2 10 3 8 5 12 7 20 15 Sales (y) 7 9 20 15 18 14 20 17 30 25 Some descriptive statistics for these data are: sx = 6.2147, sy = 6.8840 , x = 8.2, y = 17.5. Furthermore, she finds as least-squares regression equation: ŷ 8.63 + 1.0817x. 8) The correlation coefficient between Years of Experience (x) and Sales (y) is, rounded to two decimals accuracy, 0.98. True, 1.0817=b*6.8840/6.2147 5 9) A competitor’s salesperson with 10 years of experience, indicates that he may be willing to change jobs. The estimated monthly sales for this person, are, $20,000. Incorrect, 8.63+1.0817*10 10) The residual corresponding to salesperson 1 (with no years of experience) is $ 8,630. Incorrect: It should be 8,630-7,000 6 7