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WCU ECO 251 - ECO 251 First Hour Exam

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251x0451 9/30/04 ECO251 QBA1 FIRST HOUR EXAMOctober 6, 2004 Name: _____________________ Student Number : _____________________ Class Hour: _____________________ Remember – Neatness, or at least legibility, counts. In most non-multiple-choice questions an answer needs a calculation or short explanation to count.Part I. (7 points)Use the eleven numbers that you used in the second problem in the take-home exam. (If you don’t have them – take your student number plus the numbers (3, 6, 9, 9, 21) . Example: Seymour Butz’s student number is 876509, so he gets 8, 7, 6, 5, 0, 9, 3, 6, 9, 9, 21. Of course, he has read “Things That You Should Never Do on an Exam or Anywhere Else” and knows that he can’t use them this way. ) Compute the following:a) The Median (1)b) The Standard Deviation (3)c) The 2nd Quintile (2)d) The Coefficient of variation (1)1251x0451 9/30/04Part II.1. The problem in the textbook that gives the data used in the take home also gives the braking distance for a sample of domestic made cars. It is presented below.Distance(feet) frequency 210 - 220 1 220 - 230 1 230 – 240 1 240 – 250 1 250 – 260 4 260 - 270 3 270 - 280 6 280 - 290 4 290 - 300 2 300 – 310 2 310 - 320 0 Minitab was used to calculate statistics from these data. It claims the following: ,269x,5252s .61.72813k You will not be able to use any of these numbers in b) or c) without some manipulation in parts b and c. Answers below are not acceptable unless you give some evidence in the sample statistics.a) Do American cars have a shorter braking distance? Compare all 3 measures of central tendency. (2)b) Are American cars more consistent in braking distance than foreign cars? Use a dimension-free measurement of variability. (2)c) Compare the direction and degree of skewness in the two distributions. Use one dimension- free measure of skewness. (2)d) Write a 5-number summary of the results from the first take-home problem. (2) 152. The following numbers refer to miles-per-gallon of a sample of vehicles (Bowerman and O’Connell). This has been corrected.Class (mpg) f relf F relF29.8 - 30.3 ____ ____ ____ .061230.4 – 30.9 ____ ____ ____ .244931.0 – 31.5 ____ ____ 24 ____ 31.6 – 32.1 ____ .2653 35 .755132.2 – 32.7 9 .1837 46 .938832.8 – 33.3 3 .0612 49 1.000 Fill in the missing numbers. (5) 20251x0451 9/30/042Part III. (At least 22 points – 2 points each unless marked)1. Mark the variables below as qualitative (A) or quantitative (B)a) Number of days a patient stays at a spab) Preferences for 10 beers on a 1st to 10th scalec) Method of contraceptiond) Per cent change in population between censuses2. Which of the following is an example of continuous ratio data?a) Number of days a patient stays at a spab) Preferences for beers on a 1 to 10 scalec) Method of contraceptiond) Per cent change in population between censusese) None of the above. 43. A summary measure that is computed to describe a characteristic of a population is calleda) a parameter.b) a census.c) a statistic.d) An inferencee) None of the above 64. In general what are the two types of descriptive statistic most frequently reporteda) Measures of kurtosis and measures of dispersionb) Measures of kurtosis and measures of skewnessc) Measures of kurtosis and measures of central tendencyd) Measures of dispersion and measures of skewnesse) Measures of dispersion and measures of central tendencyf) Measures of skewness and measures of central tendency g) None of the above. 83251x0451 9/30/04Mark the following formulas (1 each) . Circle a, b or c. b) must be filled in if you have circled it.5. Coefficient of Excess 3442 or 442skg a) This cannot be negative. b) If this is negative it means the distribution is ______c) This can be negative, but it has no special meaning.6.  323323)2)(1(xnxxxnnnka) This cannot be negative.b) If this is negative it means the distribution is ______c) This can be negative, but it has no special meaning.7.nxxa) This cannot be negative.b) If this is negative it means the distribution is ______c) This can be negative, but it has no special meaning.8.1222nxnxsa) This cannot be negative.b) If this is negative it means the distribution is ______c) This can be negative, but it has no special meaning. 124251x0451 9/30/04Exhibit 1: The following is taken from Problem 3.22 in the text. The data below represent sales tax receipts submitted to a township government by 50 businesses in one quarter.Sales Taxes ($000)10.3 11.1 9.6 9.0 14.5 13.0 6.7 11.0 8.4 10.313.0 11.2 7.3 5.3 12.5 8.0 11.8 8.7 10.6 9.511.1 10.2 11.1 9.9 9.8 11.6 15.1 12.5 6.5 7.510.0 12.9 9.2 10.0 12.8 12.5 9.3 10.4 12.7 10.59.3 11.5 10.7 11.6 7.8 10.5 7.6 10.1 8.9 8.6The text solution manual offers the following results.(a) Stem-and-leaf display of Quarterly Sales Tax Receipts5 36 577 35688 046799 0233568910 0012334556711 01112566812 55578913 0014 515 1(b)  = 10.28(c) 2= 4.1820,  = 2.045(d) 64% of the receipts are within 1 standard deviations of the mean.(e) 94% of the receipts are within 2 standard deviations of the mean.(f) 100% of the receipts are within 3 standard deviations of the mean.9. According to the stem and leaf display, what percent of the receipts were below $7000? (1)10. If the researcher was directed to present the data in 6 classes, what should the class interval be? Show your calculations. 1511. Show the actual intervals you might use. 17Class From toA BCDEF12. The description above says that 64% of the receipts are within 1 standard deviations of the mean. Between what numbers does this mean? How does this compare with the empiricalrule? Why might there be a discrepancy? (3)13. The description above says that 100% of the receipts are within 3 standard deviations of the mean. Between what numbers does this mean? How does this compare with the Chebyshev rule? Why might there be a discrepancy? (3) 235251x0451 9/30/04Blank page for calculations.6251x0451 9/30/04 ECO251 QBA1 FIRST EXAMOctober 6, 2004TAKE HOME SECTION Name: _________________________ Student Number: _________________________Throughout this exam show


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