251x0811 (corrected) 2/25/07ECO251 QBA1FIRST EXAMFebruary 21, 2008 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) The following numbers are to be considered a sample and represent the scores of a class of ten seniors on the first exam in Dr. Hardnose’s accounting class (Doane and Seward).1x 60 88 60 71 60 73 74 75 60 99Compute the following: Show your work!a) The Median (1)b) The Standard Deviation (3)c) The 7th decile (2)d) The Coefficient of variation (1)e) (Extra Credit) Dr. Hardnose gives a second exam, but one student is absent. He enters the data from both exams into Minitab with the following results.MTB > describe c1 c2Descriptive Statistics: x1, x2 Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximumx1 10 0 ----- ---- ----- 60.00 60.00 72.00 78.25 99.00x2 9 0 72.78 2.19 6.57 65.00 65.00 74.00 79.00 79.00 The numbers computed should be self explanatory except for ‘SE Mean,’ (the standard error of the mean) which can be gotten by computing nssx. I have erased the numbers related to the statistics you shouldcompute.So – given the statistics that we have learned to compute and the facts that the mean and sample size have changed, can you compare the variability of the results of the first and second exams? (Yes or No won’t work here, give me some numbers!) 1251x0811 (corrected) 2/25/07Part II. (At least 35 points – 2 points each unless marked - Parentheses give points on individual questions. Brackets give cumulative point total.) Exam is normed on 50 points.1. Which of the following is not a measure of central tendency (2)a) The arithmetic meanb) The geometric meanc) The standard deviationd) The mediane) The mode.f) All of the above are measures of central tendencyg) None of the above is a measure of central tendency. 2. The smaller the spread of data around the mean (2)a) The smaller the interquartile rangeb) The smaller the standard deviationc) The smaller the coefficient of variationd) All of the abovee) None of the above.3. Mark the following items N (nominal), O (ordinal), I (interval) or R (ratio) data. If the data is interval or ratio data, would it be considered C (continuous) or D (discrete)? (4) [8]a) The weights of Sumo wrestlers ________b) Your Social Security number ________c) Volume of traffic on I-95 (light, medium, heavy) __________d) Number of hits in the World Series _________4. A number that is used to summarize population data is called (2)a) A parameterb) sc) A statisticd) None of the above would be used to summarize population datae) All of the above could be used to summarize population data.5. If a frequency distribution has a positive coefficient of skewness, we would expect (2) [10]a) The mean to be between the median and the modeb) The mean to exceed the medianc) The median to be larger than the mean or the mode.d) The standard deviation to exceed the meane) The coefficient of excess to be positivef) None of the above would be likely to be true. 6. Under what circumstances would you expect a population variance be zero? [12]a) If the mean is zerob) If every observation above the sample mean is precisely offset by a number the same distance below the sample mean.c) If the mean, median and mode were all the same.d) When there are an equal number of observations above and below the mediane) None of the above is likely to result in a zero population variancef) All of the above are likely to result in a zero population variance. 2251x0811 (corrected) 2/25/077. Batting averages of major league baseball players are thought to follow a symmetrical unimodal distribution with a mean of .260 and a standard deviation of .03.a) What proportion of major league players would you expect to have a batting average above .320? Why? (3)b) If you did not know that the distribution was symmetrical, what is the largest proportion of players that you would expect to have a batting average above .320? Why? (3) [18]Table 1Given below is a stem-and-leaf display of the heights in inches of 50 Christmas trees being grown for sale. The smallest tree is 44 inches. 4|44668899 5|00112244555577888899 6|000022223344557799 7|33558. In Table 1, what is the median height? (2)9. In Table 1, what are the first and third quartiles? What do they lead you to think about the skewness of the distribution? (3)10. In Table 1, assume that you were asked to present the data in 5 classes. Show how you would decide what class interval to use and list the classes below with their frequencies. (4) [27] Class FrequencyA ___ to under ___ ___B ___ to under ___ ___C ___ to under ___ ___D ___ to under ___ ___E ___ to under ___ ___3251x0811 (corrected) 2/25/07Table 2Class f relf F relF 20-35 11 .122 11 .122 35-50 .278 36 .40050-65 .70065-80 .88980-95 10 .111 90 1.00011. Fill in the missing numbers in Table 2 (3)12. Find the 31 fractile of the data in Table 2. (3) [33] 13. The Des Moines Metropolitan area consists of Dallas, Polk and Warren Counties. In the 1990 census Dallas County had 30700 people and a mean income of $9673, Polk County had 309000 people and a meanincome of $11779 and Warren County had 37300 people with a mean income of $9749. a) What is the mean income of residents of the Des Moines area? (Note: I am much more interested in how you do this that whether you get the right answer, so show your work!) (2)b) Suppose that in 1991 Census officials believe that the population and mean income in Polk county and Warren County stayed the same, but the mean income in Dallas county fell while the population stayed constant. For the Des Moines area, which of the following is likely to have occurred? (2) [37]a) The median income fell mostb) The modal income fell mostc) The mean income fell mostd) The mean, median and modal income all fell to the same degree.4251x0811 (corrected) 2/25/07 ECO251 QBA1FIRST EXAMFebruary 21, 2008TAKE HOME SECTION Name: _________________________ Student Number: _________________________Throughout this exam show your work! Please indicate clearly what sections of the problem you are answering and what formulas you
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