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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 stemandleaf 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 stemand—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 fastestgrowing companies as listed on February 17, 2002, at the Fortune magazine website. G Fastgrow a Figure 2.13 gives the MINITAB output of a stomand—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 fastestgrowing 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 FastestGrowing 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 PowerOne' 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% "3year 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 stemand—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 7201 111 24 11501 34 47 3502 70
2 7601 35 25 111301 25 4a 3502 s7
3 71101 23 26 112101 22 49 3602 111
4 71201 42 27 112301 14 so 3602 92
5 71501 54 28 112501 20 51 3602 95
6 72701 50 29 12101 32 52 3602 85
7 11101 41 30 12301 27 53 3702 113
8 01301 12 31 121001 23 54 3702 102
9 02001 3 32 122001 35 55 31302 23
1o 02001 11 33 122301 29 56 32702 11
11 828—01 11 34 123101 25 57 4102 8
12 9301 31 35 123101 10 50 41102 11
13 91001 35 36 123101 15 59 41502 35
14 91701 14 37 1502 23 so 41902 29
15 91301 14 3a 1302 . 26 61 5202 so
16 32901 27 39 11502 30 52 51502 18
17 10401 14 40 11002 36 A 63 52502 58
10 10601 23  41 12202 42 54 541432 4
19 101501 47 42 12502 45 65 61202 5
20 102301 17 43 12702 43 56 62402 1 5
21 102501 21 44 2502 39 07 132502 13
22 103001 18 45 2902 53
23 11201 31 46 22302 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—andleaf display and runs plot of the numbers of missed shots. Do you think that Ihe stemmedleaf 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 stemandleafdisplay 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.IIowlikely
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 fastestglowing 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 McGrawHlll
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
049 2
50—99 10
100—149 “I
150—199 0
zoo249 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 yearfrom 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: ﬁom 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 fastestgrowmg 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 fastestgrowmg 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 zscore 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 30year rates
and 15year rates (expressed as annual percentage rate orAPR) and. ifthere is. what is the size of
that difference. The table on the uextpagedisplays the 30yearrate and the 15year rate for each of
eight randomly selected lending institutions. Also given is the difference between the 30year rate and the 15year rate for each lending institution. To the left of the table are given sideby—sidc
MINI'I‘AB boxand—whiskers plots of the 30year rates and the 15year rates and a NﬂNITAB
boxand—whiskers plot of the differences between the rates. Use the boxand—whiskers plots to
compare the 30year rates and the 15year rates. Also, calculate the average of the differences
between the rates. a Mortgage Annual Percentage Rate Lending Institution 30wYear 15Year 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: BestPerforming 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 56 115
Lowe‘s Companies 4.4 18.7 946 12.6
Men's Wearhouse 4.9 3.0 65 12.7
Midreels 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
WellMart Stores 3.1 12.9 6435 15
Walgreen 3.6 16.1 886 20.3
WilliamsSomme 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 StemandLeaf Display of the 30 Revenue Growth
Rates Stenand~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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 Standard Deviation, Bar chart, Percentage point

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