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EcondataT1question - Econ1003 Analysis of Economic Data...

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Unformatted text preview: Econ1003 Analysis of Economic Data Tutorial One Chapter 2 Review questions 7 2.3 2.4 :23: 7. 2002, issue. Forbes published the Forbes Platinum List of the best- omung. g compames in a variety industry groupings, as picked by the minds editors. Table 2.4 gives the Forbes Platinum List for the retailing industry. a Forbeslfl‘agt a a stem-and-leaf display of the profit margin percentages for the retailers in the Plat. tnumLtst. Usedrewholenumbets from 1 to 12115 thestetna'lhendescrihethedisu'ibutionof profit margins. 1! Construct a stem-and—leaf display of the return on capital percentages for the retailers in the Plat- inum List. Use the whole numbers from it) to 39 as the stems. Then describe the distribution of the returns. 1'. Compare the distributions of the profit margins and return on capital percentages. The data in 'Ihble 2.5 concern the 3G fastest-growing companies as listed on February 17, 2002, at the Fortune magazine website. G Fastgrow a Figure 2.13 gives the MINITAB output of a stom-and—leaf display of the revenue growth rates for the 30 firms using the stems 30. 40. 50. 60. 70, 80, 90, 100, 110. 120, 130, I40, 150, 160, 170, and 180. Describe the shape of the distribution ofgrowth rates. b The priedeamings ratio of a firm is a multiplier applied to a firm’s earnings per share (EPS) to determine the value of the firm’s common stock. For instance, if a firm's earnings per share is $5. and if its pricelearnings ratio (or PIE ratio) is 10, then the market value of each share of common stock is (5)00) = $50. To quote Stanley B. Block and Geoffrey A. Him in their book Foundations of Financial Management? The PIE ratio indicates expectations about the future of a company. Firms expected to pro- vide renrms greater than mose for the market in general with equal or less risk ofien have PIE ratios higher than the market PIE ratio. - In the figure below we give a dot plot of the PIE ratios for 24 of the 30 fastest-growing compa- nies (the PIE ratios for 6 of the companies were not available to Fortune). Describe the distribu- tion of PIE. ratios. PIE Ratio c Construct a dot plot of the total return percentages for the 30 fastest—growing companies and describe the distribution of return percentages. TA 3 r. E 2.5 Data Concerning the 311 Fastest-Growing Companies as Listed on February 17. 2002. at the Fortune Magazine Website @ FastGrow EPS Revenue Total EPS Rank Company Growth* Growth* Return* Rank Company Growth“ Growth“ 1 acids Entertainment 242% 128% 89% 17 Verity 122% 52% 2 - Siehel Systems 155% 106% 80% 18 Integrated Electrical 670% 125% 3 Calpine 74% 101% 147% Services’ 4 Andra: 224% 54% 103%l 18 Stericycle' 64% 100% 5 Measurement Specialties 204% 53% 124% 20 magic ' 50% 66% 6 TranSwitch 263% 77% 53% 21 Metro One 46% 811% 7 Triouint Semiconductor 93% 60% 92% Te‘emmmumcaflom 8 Immunex 973% 76% 48% 22 Anadarko Petroleum' 32% 130% 9 Mercury Interactive 35% 59% 75% 22 Sum“ Mame" 69% 55% 10 Network Appliance 92% 89% 41 r“. 24 Affiliated Managers 137% 70% 11 Advanced Digital 132% 51% 69% 25 Fm“ Labmm'ies 33% 45% tnfomration 26 Monterey Pasta 147% 31 '15 12 Chico‘s PAS 97% 50% 79% 27 Jakks Pacific’ 67% 85% 13 Hot Topic 78% 56% 74% 27 Power-One' 43% 86% 14 Zomax 93% 35% 32% 29 Quanta Services 55 % 183% 15 Elantec Semiconductor' 83% 45% 129% 30 United Rentals 209% “3% 15 Sonic Automotive' 79% 1 15% 32% "3-year annual rate. Revenue Total Return“ 55% —21 % 48% 144% 102% 18% 58% 18% 58% 87% 32% 74% 31 16 -15% 2.8 Consider Table 1.9 (page 18). which gives the numbers of days needed to settle 67 homeowners' insurance claims. a ClaimSet a Construct a stem-and—leaf display using the stems 00, 10. 20, . . . , 90, 100. ill). b Figure 2.21 gives theWI'DKBonlputofafiequency hismgmm ofthe67 numbers 11st to seflleVefifymattheclassesandclassfi'equenciesusedinFigure221memoseoblainedby using the histoyam consuuction method discussed in this section. 1: Ufingflwmand—lmfdisphyandmefimmdesm‘bemefismfimofmenmmofdays mseuleWhatcansedmedism'hlfionmlooklikelhis(seeExemise 1.16011pages 17211618)? W TA 11 LE 1.9 Number of Days Required to Settle Homeowners Insurance Claims (Claims Made from July 2. 2001 to June 25. 2002) 6 ClaimSet Days to Days to Days to Claim Loss Date Settle Claim Loss Dane Settle Claim Loss Date Settle 1 7-2-01 111 24 11-5-01 34 47 3-502 70 2 7-6-01 35 25 11-13-01 25 4a 3-5-02 s7 3 7-11-01 23 26 11-21-01 22 49 3-6-02 111 4 7-12-01 42 27 11-23-01 14 so 3-6-02 92 5 7-15-01 54 28 11-25-01 20 51 3-6-02 95 6 7-27-01 50 29 12-1-01 32 52 3-602 85 7 11-1-01 41 30 12-3-01 27 53 3-7-02 113 8 0-13-01 12 31 12-1001 23 54 3-7-02 102 9 0-20-01 3 32 12-20-01 35 55 3-1302 23 1o 0-20-01 11 33 12-23-01 29 56 3-27-02 11 11 8-28—01 11 34 12-31-01 25 57 4-1-02 8 12 9-3-01 31 35 12-31-01 10 50 4-11-02 11 13 9-10-01 35 36 12-31-01 15 59 4-15-02 35 14 9-17-01 14 37 1-5-02 23 so 4-19-02 29 15 9-13-01 14 3a 1-3-02 . 26 61 5-2-02 so 16 3-29-01 27 39 1-15-02 30 52 5-15-02 18 17 10-4-01 14 40 1-10-02 36 A 63 5-25-02 58 10 10-6-01 23 - 41 1-22-02 42 54 541432 4 19 1015-01 47 42 1-2502 45 65 6-12-02 5 20 10-23-01 17 43 1-27-02 43 56 6-24-02 1 5 21 10-25-01 21 44 2-5-02 39 07 13-2502 13 22 10-30-01 18 45 2-9-02 53 23 11-2-01 31 46 2-23-02 64 2.12 A basketball player practices free 111100113 by taldng 25 shots each day, and he records the number of shots missed each day in order to track his progress. The numbers of shots missed on days I through 30 are, respectively. l7. 15, 16, 18. 14. 15, 13, 12, 10, ll, 11, 10, 9, 10, 9. 9, 9. 10. 8, 10. 6, 8, 9, 8, 7, 9, 8, 1. 5. 8. Conslsuct a mm—and-leaf display and runs plot of the numbers of missed shots. Do you think that Ihe stemmed-leaf display is representative of the numbers of 511015 that the player will miss on future days? Why or whyoot? a FreeThrw 2.36 In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner coats for four people) from expense reports submitted by members of the sales force. $157 $132 $109 $145 $125 $139 a Calculate E. :2. and .r for the expense dam. In addition. show that the two different fonnulas for calculating :2 give the same result. I) Assuming that the distribution of entertainment expenses is approximame annually distributed, calculate estimates of tolerance intervals containing 68.26 percent. 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force. I: If a member of the sales force submits an entertainment expense (dinner- cost for four} of $190, should this expense be considered unusually high (and possibly worthy of investigation by the company)? Explain your answer. d Compute and interpret the z—score for each of the six entertainment expenses. 2.38 THE BANK CUSTOMER WAITING TIME CASE 0 WaitTtme The mean and the standard deviation of the sample of 100 bank customer waiting times are E = 5.46 and: = 2.475. a What do the stem-and-leafdisplay and histogram in Figures 2.16 and 2.17 (page 52) say about whether the Empirical Rule should be used to describe the bank customer waiting times? it Use the Empirical Rule to calculate estimates of tolerance intervals containing 68.26 percent. 95.44 percent, and 99.73 percent of all possible bank customer waiting times. I: Does the estimate of a tolerance interval containing 68.26 percent of all waiting times provide evidence that at least two~tllirds of all customers will have to wait less than eight minutes for service? Explain your answer. (I How do the percentages ofthe 100 waiting times in'Ihble 1.6 (page 11) that acmally fall into the intervals 5 i s], [It I 25], andfi : 3:] compare to those given by the Empirical Rule? Dothesecomparisons indicate tint drestatisticalinferencesyoumade inpartsbandcatc reasonably valid? 2.54 a In a poll released by the Gallup Organization on January 4, 2000, 622 randomly selected adults Were asked the following question on December 28, 1999. As you may know, most computer systems around the world have to be reprogrammed somattheycanaceuratelyrecognizethedateoncewereachtheYearZOOO.I-Iowlikely do you think it is that there will be major problems in the United States this New Years as a direct or indirect result of the Y2K computer problem—very likely, somewhat likely, somewhat unlikely, or very unlikely? The poll’s results were as follows: Very likely (7%). Somewhat likely (30%), Somewhat unlikely (32%), Very unlikely (30%), No opinion (1%).” Use these data to construct a bar chart and a pie chart. What actually happened? h 01" the 100 fastest-glowing companies in America as given in the September 28, 1998, issue of Farting, there were 22 energy companies, 20 industrial companies. 10 retail companies, 8 health care companies, 5 financial service companies, 26 technology companies, and 9 other companies. Use these data to construct a pie chart and a bar chart. 2.62 In the book Essentials of Marketing Research, William R. Dillon. ‘I‘homas J. Madden, and Neil H. Firtle present a scatter plot of the number of units sold of 20 varieties of a canned soup versus the amount of shelf space allocated to each variety. The Scatter plot is shown in Figure 2.48. a Does there appearto be a relationship between y (units sold) andx (shelf space)? Does the rela- tionship appear to be straight line (linear) or curved? How does y (units sold) change as x (shelf space) increases? is If you were told that a variety of soup is allotted a small amount of shelf space, what would you guess about sales? I: Do you think that the amount of shelfspace allocated to a variety causes sales to be higheror lower? Give an alternative explanation for the appearance of the scatter plot. nouns 2.48 A Scatter Plotofthiits Sold versus Shelf Space UNITSSOLD Y” ' A SHELF SPACE X Source in. R. Dillon. 1'. 1. Madden. and N. H. firtle. ," Essentials ofMarkeohg Research (Burr Ridge. IL' Iidmd I3. Innin. Inc. 1993). pmcmm 61903. Reprinted bypennission of McGraw-Hlll Companis. int. @523- 2.14 The following is a frequency dism'bution summarizing Menus growth data for the 20 fastest- growing firms as given on Fortune magazine’s Website (as of August 7, 2001). Revenue Growth (Patent) Frequency 0-49 2 50—99 10 100—149 “I 150—199 0 zoo-249 1 Source: httpzllwwwjortunexom, August 7. 2001. Calculate the (approximate) population mean. variance. and standard deviation for these data. 2.80 The Standard and Poor’s 500 stock index is a commonly used measure of stock market perfor- mance in the United States. In the table below, we give the value of the S & P500 index on the first day ofmarket trading for each year-from 1997 to 2002. Year 58:? 500 Index 1997 737.01 1998 975.04 1999 1228.10 2000 1,455.22 2001 1,283.27 2002 1,154.61 Source: httpfltableiinanceyahoo.com. a Show that the percentage changes (rates of return) for the S&P 500 index for the years from 1997 to 1998 and from 1998 to 1999 are, respectively, 32.3 percent and 26.0 percent (that is. .323 and .260 expressed as decimal factions). I: Find the rates ofrehim for the 8&P500index for each oftheyears: fi-om 1999 to 2000; from 2000 to 2001; from 2001 to 2002. I: Calculate the geometric maximum for the 3&P500 index over the period from 1997 to 2002. ‘ (1 Suppose that an investment of $1,000,000 is made in 1997 and that the portfolio performs with teams equal to those of the 8&1” 500 index. What is the investment portfolio worth in 2002‘? Di fluent: 6.9 63 6.7 65 65 5.4 63 62 6.1 F w P h.- 0.1 2.15 Calculate the mean, median. and mode of each of the following populations of numbers: a 9. 8.10.10.12.65, 11,10,128 b 110, 120, 70, 90, 90. 100, 80, 130, 140 _ _ 2 i9 Consrder'l'able 2.5 (page 50), which gives data concerning the 30 fastest-growmg comparues as listed on February 7, 2002. at the Fortune magazine website. 0 FastGrow . a The mean and median of the EPS (earnings per share) growth percentages tor the 30 fastest- growing companies can be found to be 160.7 and 92.5 respectively. By exarmnrng the apltual EPS growth percentages in Table 2.5, explain why the mean is much larger than the me ran. h The mean and median of the total return percentages for the 30 fastest-growmg companies can be found to be 65.2 and 63.5, respectively. By examining the actual total return percent- ages in Table 2.5, explain why the mean and median are nearly equal. 2.33 Consider the following population of five numbers: 5. S. 10. 12. 15. Calculate the range. variance, and standard deviation of this population. 2.35 Table 2.11 gives data concerning the top 10 U.S. airlines (ranked by revenue) as listed on the Fortune magazine website on February 14. 2002. 9 AirRev a Calculate the population range, variance. and standard deviation of the 10 revenues and of the 10 profits (note that values in parentheses are negative—that is. losses rather than profits). b Using the population of profits. compute and interpret the z-score for each airline. 2.41 In the article “The Best Mutual Funds for a Volatile Future” in the December 21. 1998. issue of Fortune, Julie Creswell reports that the mean yearly return for the Westwood Balanced mutual fund is 17.3 percent with a standard deviation of 10 percent. She also reports that the mean yearly return for the Green Century Balanced fund is 9.33 percent with a standard deviation of 22.4 percent. a For each mutual fund. find an interval in which you would expect 95 .44 percent of all yearly returns to fall. Assume returns are normally distributed. b Using the intervals you computed in part a. compare the two mutual funds with respect to average yearly returns and with respect to variability of returns. c Calculate the coefficient of variation for each mutual fund. and use your results to compare the funds with respect to risk. Which fund is riskier? 3.1}? On its website, the Statesman Journal newspaper (Salem. Oregon, 1999} reports mortgage loan interest rates for 30—year and 15—year fixed—rate mortgage loans for a number of Willamette Valley lending institutions. Of interest is whether there is any systematic difference between 30-year rates and 15-year rates (expressed as annual percentage rate orAPR) and. ifthere is. what is the size of that difference. The table on the uextpagedisplays the 30-yearrate and the 15-year rate for each of eight randomly selected lending institutions. Also given is the difference between the 30-year rate and the 15-year rate for each lending institution. To the left of the table are given side-by—sidc MINI'I‘AB box-and—whiskers plots of the 30-year rates and the 15-year rates and a NflNITAB box-and—whiskers plot of the differences between the rates. Use the box-and—whiskers plots to compare the 30-year rates and the 15-year rates. Also, calculate the average of the differences between the rates. a Mortgage Annual Percentage Rate Lending Institution 30wYear 15-Year Difference American Mortgage N.W. Inc. 6.715 6.599 0.116 City and Country Mortgage 6.648 6.367 0.281 Commercial Bank 6.740 6.550 0.190 Landmark Mortgage Co. 6.597 6.362 0.235 Liberty Mortgage. Inc. 6.425 6.162 0.263 MaPS Credit Union 6.880 6.583 0.297 Mortgage Brokers, Inc. 6.900 6.800 0.100 Mortgage First Corp. 6.675 6.394 0.281 Silver Eagle Mortgage 6.790 6.540 0.250 Source: Via World Wide Web, Salem Homeplace Mortgage Rates Directory, http:/I‘wwwsalemhomeplace.cornlpageslfinancei, January 4. 1999. Reproduced by permission of the Statesman Journal newspaper, Salem, Oregan. 2.67 In the article “How to Display Data Badly" in the May 1984 issue of The American Statistician. Howard Wainer presents a stocked bar chart of the number of public and private elementary Schools (1929—1970). This bar chart is given in Figure 2.54. Wainer also gives a line graph of the number of private elementary schools (1930—1970). This graph is shown in Figure 2.55. 9.) Looking at the bar chart of Figure 2.54, does there appear to be an increasing trend in the num- ber of private elementary schools from 1930 to 1970? b Looking at the line graph of Figure 2.55. does there appear to be an increasing trend in the number of private elementary schools from 1930 to 1970‘? Which portrayal of the data do you think is more appropriate? Explain why. Is either portrayal of the data entirely anDrODriate? Exolain. 3.0 W TA 3 1. E 2.4 The Forbes Platinum fist: Best-Performing Retailers as Listed In the January 7. 2002, Issue of Forbes Magazine a ForbesPiat Profit Sales Growth ‘16 Net Income (S Millions) Return on Capital (96) Company Margin ('56) (Last 12 Months) (Last 12 Months) (Last 12 Months) Abercrombie & Fitch 12.5 14.7 161 39.4 American Eagle Outfitters 8.3 39.4 111 28.5 Bed 31111 3 Beyond 7.2 25 189 23.1 Best Buy 2.3 25.0 387 19.? 01': Wholesale Club 1.5 11.5 81 12 Burlington Coat 2.7 8.8 65 10.3 CDW Computer Centers 4.2 11.3 159 26.5 Costco Wholesale 1.1 8.2 602 11.8 cvs 3.5 10.1 153 15.1 Dollar Tree Stores 6 21 A 112 20.3 Famin Dollar Stores 5.2 17 190 22.8 Home Depot 5.5 13.7 2799 16.“) Insight Enterprises 2.3 9.6 48 16.5 Kohl's 6.3 26.2 440 15.3 lelted 4.4 —1.2 431 17.4 Llnens ‘n Things 3.2 16.1 56 11-5 Lowe‘s Companies 4.4 18.7 946 12.6 Men's Wearhouse 4.9 3.0 65 12.7 Mid-reels Stores 3.3 15.1 18 ‘ 10.3 ; Pier 1 Imports 5.9 10.7 as 15.7 111111115th 5.7 5.3 277 23 Ross Stores 5.2 11.2 150 30.5 1; Sonic Automotive 1.1 7.3 70 10.3 Starbucks 6.8 22.1 ' 101 15.4 sum Mart 1.9 10.4 24 11.7 g. 3 1111191: 1.7 10.3 123 20.3 1 Target 3.2 9.6 1253 11.3 flffany 10.9 ——2.1 176 15.8 L 11x Companies 4.1 9.6 480 32.2 Well-Mart Stores 3.1 12.9 6435 15 Walgreen 3.6 16.1 886 20.3 Williams-Somme 2.5 17 50 10.9 Source: Reprinted by permission of Forbes magazlne. o 2002 Forbes. Inr. FIG U 11 E 2.15 Excel Output of a Frequency Histogram of the 65 Satisfaction Ratings FIG u R E 2.16 Excel Output of a Frequency Histogram of the 100 Waiting Times 3‘ = II 3 U- 0 I- II- I n m TA B L E 2.11 The Top 10 Airlines (Ranked by Revenue) in 2001 i) AirRev Revenue Profits Company (5 Billions) (5 Millions) American Airlines 20.2 813 United Airlines 19.4 50 Delta Airlines 15.9 1.303 Northwest Airlines 11.4 256 Continental Airlines 9.9 342 US Airways Group 9.3 (269) Southwest Airlines 5.6 603 Trans World Airlines 3.5 (387) America West Holdings 2.3 2 Alaska Air Group 2.2 (70) Source: "Top Ten Airlines in 2001," Fortune 500, April 16. 2002. Copyright o 2002 Time. Inc. All rights reserved. M TA 13 L E 1.6 Waiting Times (in Minutes) for the Bank Customer Waiting Time Case 0 WaitTime 1.6 6.2 3.2 5.6 7.9 6.1 7.2 6.6 5.4 6.5 4.4 1.1 3.8 7.3 5.6 4.9 2.3 4.5 7.2 10.7 4.1 5.1 5.4 8.7 6.7 2.9 7.5 6.7 3.9 .8 4.7 8.1 9.1 7.0 3.5 4.6 2.5 3.6 4.3 7.7 5.3 6.3 6.5 8.3 2.7 2.2 4.0 4.5 4.3 6.4 6.1 3.7 5.8 1.4 4.5 3.8 8.6 6.3 .4 8.6 7.3 1.8 5.1 4.2 6.8 10.2 2.0 5.2 3.7 5.5 5.8 9.8 2.8 8.0 8.4 4.0 3.4 2.9 11.6 9.5 6.3 5.7 9.3 10.9 4.3 1.3 4.4 2.4 7.4 4.7 3.1 4.8 5.2 9.2 1.8 3.9 5.8 9.9 7.4 5.0 FIG u n E 2.54 Wainer's Stacked Bar Chart Fl G u R E 2.55 Wainer‘s Line Graph _| In B Public - Private .5 O O .- «b a w _. N Schools (in thousands) 0 Schools (in thousands) 8 §V c9” éV ’8 \q \9 Ln School year 0 1930 1940 1950 1960 1970 W F I G u n E 2.13 MINITAB Output of a Stem-and-Leaf Display of the 30 Revenue Growth Rates Sten-and~laaf of Rev Growth: N=30 Laaf Unit = 1.U l a 1 a n 55 11 5 umaausaq 13 5 na' (u) 7 0575 13 a usuaa a a a ID 035 5 "LL 5 u 12 55 a 13 u l 1H 1 15 1 IE ‘ L L? l 15 3 ...
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EcondataT1question - Econ1003 Analysis of Economic Data...

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