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Data and StatisticsLearning Objectives Obtain an appreciation for the breadth of statistical applications in business and economics. Understand the meaning of the terms elements, variables, and observations as they are used istatistics. n Obtain an understanding of the difference between categorical...

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Cha pt e r1 Da t aandSt a t i s t i c s

Le a r ni ngObj e c t i ve s 1 .

Obt a i na na p pr e c i a t i onf ort hebr e a dt ho fs t a t i s t i c a la p pl i c a t i onsi nb us i ne s sa nde c on omi c s .

2 .

Un de r s t a ndt heme a ni ngo ft het e r mse l e me nt s ,v a r i a b l e s , a ndo bs e r v a t i o nsa st h e ya r eus e di n s t a t i s t i c s .

3 .

Obt a i na nun de r s t a nd i n go ft hedi ffe r e nc ebe t we e nc a t e go r i c a l , qua nt i t a t i ve , c r os s e c t i o na la n dt i me s e r i e sda t a .

4 .

Le a r na bo utt h es ou r c e sofd a t af ors t a t i s t i c a la na l y s i sbot hi nt e r na la nde x t e r na lt ot h efir m.

5 .

Bea wa r eo fho we r r o r sc a na r i s ei nd a t a .

6 .

Kno wt h eme a ni n gofd e s c r i pt i v es t a t i s t i c sa nds t a t i s t i c a li nf e r e n c e .

7 .

Bea b l et odi s t i n gui s hb e t we e napo pu l a t i ona n das a mp l e .

8 .

Un de r s t a ndt her o l eas a mpl ep l a y si nma k i n gs t a t i s t i c a li nf e r e nc e sa bo utt hepo pu l a t i o n.

9 .

Kno wt h eme a ni n goft h et e r md a t ami ni n g .

1 0.

Bea wa r eo fe t h i c a lgu i de l i ne sf o rs t a t i s t i c a lpr a c t i c e .

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Cha pt e r1

Sol ut i o ns : 1 .

2.

St a t i s t i c sc a nber e f e r r e dt oa snu me r i c a lf a c t s .I nab r oa de rs e ns e ,s t a t i s t i c si st h efie l do fs t ud y d e a l i n gwi t ht hec ol l e c t i on ,a na l y s i s , pr e s e n t a t i o na ndi nt e r p r e t a t i o no fda t a . a.

The ten elements are the ten cars

b.

5 variables: Size, Cylinders, City MPG, Highway MPG, and Fuel

c.

Categorical variables: Size and Fuel Quantitative variables: Cylinders, City MPG, and Highway MPG

d. Variable Size Cylinders City MPG Highway MPG Fuel 3.

Measurement Scale Ordinal Ratio Ratio Ratio Nominal

a.

Average mpg for city driving = 182/10 = 18.2 mpg

b.

Average mpg for highway driving = 261/10 = 26.1 mpg On average, the miles per gallon for highway driving is 26.1 – 18.2 = 7.9 mpg greater compared to city driving.

c.

3 of 10 or 30% have four cylinder engines

d.

6 of 10 or 60% use regular fuel

4 . a.

The seven elements are the seven schools shown

b.

5 variables: State, Campus Setting, Endowment, Applicants Admitted, and NCAA Division

c.

Categorical variables: State, Campus Setting, and NCAA Division Quantitative variables: Endowment and Applicants Admitted

5.

6.

a.

Average endowment = 74.6/7 = $10.657 billion

b.

Average percentage admitted = 111/7 = 15.86%

c.

3 of 7 or 42.9% have NCAA Division III varsity teams

d.

3 of 7 or 42.9% have a City: Midsize campus setting

a.

Quantitative

b.

Categorical

c.

Categorical 1-2 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Da t aa ndSt a t i s t i c s

7.

8.

d.

Quantitative

e.

Categorical

a.

Each question has a yes or no categorical response.

b.

Yes and no are the labels for the customer responses. A nominal scale is being used.

a.

1015

b.

Categorical

c.

Percentages

d.

.10(1015) = 101.5 101 or 102 respondents said the Federal Bank is doing a good job.

9 . a . Ca t e g or i c a l b .3 0of7 1 ;4 2. 3% 10. a.

Categorical

b.

Percentages

c.

44 of 1080 respondents or approximately 4% strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving.

d.

165 of the 1080 respondents or 15% of said they somewhat disagree and 741 or 69% said they strongly disagree. Thus, there does not appear to be general support for allowing drivers of motor vehicles to talk on a hand-held cell phone while driving.

1 1.a . Qua nt i t a t i v e ;r a t i o b . Ca t e g o r i c a l ;no mi na l c . Ca t e g o r i c a l ;or di na l d . Qua nt i t a t i v e ;r a t i o e . Ca t e g or i c a l ;o r di n a l .Th er e s p ons et ot h i sq u e s t i onwa sr e c o r de da san ume r i c a lv a l uef r o m1t o10 . Wh i l et h eda t aa r enu me r i c a l ,t he ya r en o tq ua nt i t a t i v e .Thenume r i c a lv a l u e sf r om1t o1 0r e p r e s e nt c a t e g or i e st h a to r de rt heo v e r a l lr a t i n gs o me whe r ebe t we e nu na c c e p t a bl ea ndt r u l ye x c e p t i o na l .Th e d a t ama yb eo r d e r e db yr e s p ons ec a t e g or ywi t hahi ghe rnu mbe rc a t e g or yi n di c a t i n gah i g he ro v e r a l l r a t i n g . Wh i l ewepr e f e rt hec a t e g or i c a l ;or di na la ns we ra bo v e , a tt i me ss t a t i s t i c i a nsma ymak et he a s s u mpt i ont h a tt h enu me r i c a lr e s p o ns e sa r ee qua l i nt e r v a lme a s u r e sonaq u a nt i t a t i v es c a l ef r om1t o 1 0.Whe nt hi sa s s ump t i oni sma de ,t hed a t ama ybec on s i de r e dqu a nt i t a t i v ewi t ha ni n t e r v a ls c a l eof me a s u r e me nt .I nt hi sc a s e ,a ddi t i on a ls t a t i s t i c a lc omp ut a t i on ss u c ha st h ea v e r a g eo v e r a l lr a t i n g b e c o mehe l p f uli ns umma r i z i n gt hed a t a . 1-3 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cha pt e r1

1 2.a . Th epop ul a t i o ni sa l lv i s i t o r sc o mi n gt ot h es t a t eo fHa wa i i . b .S i nc ea i r l i nefli ght sc a r r yt hev a s tma j o r i t yofvi s i t o r st ot h es t a t e , t heus eofqu e s t i on na i r e sf or p a s s e n g e r sd ur i n gi n c omi n gfli ght si sag oo dwa yt or e a c ht hi spo pu l a t i o n.Theq u e s t i on na i r ea c t ua l l y a ppe a r so nt h eba c kofama nd a t o r yp l a nt sa n da ni ma l sd e c l a r a t i o nf or mt ha tpa s s e n g e r smu s t c omp l e t edur i n gt h ei nc omi n gfli gh t .Al a r g epe r c e nt a g eo fpa s s e n g e r sc o mpl e t et h ev i s i t or i n f o r ma t i onq u e s t i on na i r e . c . Que s t i on s1a nd4p r o v i deq ua n t i t a t i v eda t ai n di c a t i n gt henu mbe rofv i s i t sa n dt hen umb e ro fda y si n Ha wa i i .Qu e s t i on s2a nd3p r o vi dec a t e g or i c a lda t ai n di c a t i n gt hec a t e g o r i e so fr e a s onf o rt h et r i p a ndwhe r et hev i s i t orpl a n st os t a y . 13. a.

Federal spending measured in trillions of dollars

b.

Quantitative

c.

Time series

d.

Federal spending has increased over time

14. a.

The graph of the time series follows: 350

Cars in Service (1000s)

300 250 200 Hertz Dollar Avis

150 100 50 0 2006

2007

2008

2009

2010

2011

Year

b.

In 2007 and 2008 Hertz was the clear market share leader. In 2009 and 2010 Hertz and Avis have approximately the same market share. The market share for Dollar appears to be declining.

1-4 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Da t aa ndSt a t i s t i c s

c.

The bar chart for 2010 is shown below. 350

Cars in Service (1000s)

300 250 200 150 100 50 0

Hertz

Dollar

Avis

Company This chart is based on cross-sectional data. 1 5.a . Quantitative – number of new drugs approved b.

Time series

c.

July; 1100

d.

2.9%; Yes, because most recreational boating takes place during the summer months.

e.

The bar graph follows the shape of a bell curve.

1 6.

The answer to this exercise depends on updating the time series of the average price per gallon of conventional regular gasoline as shown in Figure 1.1. Contact the website www.eia.doe.gov to obtain the most recent time series data. The answer should focus on the most recent changes or trend in the average price per gallon.

1 7.

I n t e r n a lda t aons a l a r i e so fo t he re mpl o y e e sc a nbeob t a i ne df r o mt h epe r s o nne lde pa r t me n t . Ex t e r na lda t ami gh tb eob t a i ne df r o mt h eDe pa r t me ntofLa b orori n dus t r ya s s o c i a t i ons .

1 8.a . 684/1021; or approximately 67% b . 612 c.

Categorical

1 9.a . Al ls u b s c r i b e r so fBu s i ne s sWe e ki nNo r t hAme r i c aa tt het i met h es ur v e ywa sc on duc t e d. b . Qu a n t i t a t i v e c . Ca t e g o r i c a l( y e so rn o) 1-5 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Cha pt e r1

d . Cr os s e c t i on a l-a l lt h eda t ar e l a t et ot h es a met i me . e . Us i n gt hes a mp l er e s ul t s , wec o ul di nf e ro re s t i ma t e59 %o ft hepop ul a t i ono fs ub s c r i b e r sh a v ea n a nnua li nc o meo f$ 75, 0 00ormo r ea n d50 % oft h ep opu l a t i ono fs u bs c r i be r sh a v ea nAme r i c a n Ex p r e s sc r e d i tc a r d. 2 0.a .4 3% ofma na g e r swe r eb ul l i s horv e r yb ul l i s h. 2 1% ofma na g e r se xp e c t e dhe a l t hc a r et obet h el e a d i n gi ndu s t r yo v e rt hen e x t1 2mon t hs . b . Wee s t i ma t et h ea v e r a g e12 mo nt hr e t ur ne s t i ma t ef ort h ep op ul a t i ono fi n v e s t me ntma na g e r st ob e 1 1. 2%. c . Wee s t i ma t et h ea v e r a g eo v e rt hep opu l a t i ono fi n v e s t me ntma na g e r st obe2. 5y e a r s . 2 1.a . Thet wop opu l a t i onsa r et hep op ul a t i onofwome nwh os emo t he r st o okt hed r ugDESdur i n g p r e g na nc ya ndt hep op ul a t i ono fwo me nwhos emot he r sd i dn o tt a k et hedr u gDESd ur i n gpr e gn a nc y . b .I twa sas u r v e y . c .6 3/3 . 9 80=15. 8wome no utofe a c h10 00de v e l op e dt i s s u ea b nor ma l i t i e s . d . Th ea r t i c l er e p or t e d“ t wi c e ”a sma n ya bno r ma l i t i e si nt hewome nwho s emot h e r sh a dt a k e nDES d ur i n gpr e gna nc y .Th us , ar o u ghe s t i ma t ewou l db e15. 8 / 2=7. 9a b no r ma l i t i e sp e r100 0wome n who s emo t he r sh a dn ott a ke nDESdur i n gp r e g na n c y . e .I nma n ys i t ua t i on s ,d i s e a s eoc c ur r e nc e sa r er a r ea nda ffe c to nl yas ma l lpo r t i o noft h epop ul a t i o n. La r g es a mpl e sa r ene e de dt oc ol l e c tda t aonar e a s ona b l enumb e ro fc a s e swh e r et h ed i s e a s ee x i s t s . 22. a. b.

The population consists of all customers of the chain’s stores in Charlotte, North Carolina. Some of the ways that could be used to collect the data are as follows:  Customers entering or leaving the store could be surveyed  A survey could be mailed to customers who have a shopper’s club card for the stores  Customers could be given a printed survey when they check out  Customers could be given a coupon that asks them to complete a brief on-line survey; if they do, they will receive a 5% discount on their next shopping trip.

23. a.

This finding is applicable to the population of all American adults.

b.

This finding is applicable to the population of American adults that own a cellphone and/or a tablet computer.

c.

They conducted a sample survey. It would be way too costly to survey all American adults or all American adults who own cellphones and/or tablet computers. As we will see later in the text, very good results can be obtained using a sample survey.

d.

These results should be quite interesting to restaurant owners. It suggests that it would be worthwhile for them to have a website and to consider advertising through an internet search company, such as Google. 1-6 © 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Da t aa ndSt a t i s t i c s

2 4.a . Th i si sas t a t i s t i c a l l yc o r r e c tde s c r i p t i v es t a t i s t i cf ort h es a mp l e . b . Ani nc o r r e c tg e ne r a l i z a t i ons i nc et heda t awa sn o tc o l l e c t e df o rt h ee n t i r epop ul a t i o n. c . Ana c c e p t a b l es t a t i s t i c a li nf e r e n c eba s e do nt heu s eoft hewo r d“ e s t i ma t e . ” d . Wh i l et hi ss t a t e me nti st r uef ort hes a mp l e , i ti sno taj us t i fia bl ec onc l u s i onf ort h ee n t i r epo pul a t i o n. e . Thi ss t a t e me n ti sno ts t a t i s t i c a l l ys u pp or t a b l e .Whi l ei ti st r u ef o rt hepa r t i c ul a rs a mp l eo bs e r v e d ,i t i se n t i r e l ypo s s i bl ea n de v e nv e r yl i k e l yt ha ta tl e a s ts o mes t ud e nt swi l lb eou t s i d et he6 5t o90r a n g e o fgr a de s . 2 5.a.

b.

There are five variables: Exchange, Ticker Symbol, Market Cap, Price/Earnings Ratio and Gross Profit Margin. Categorical variables: Exchange and Ticker Symbol Quantitative variables: Market Cap, Price/Earnings Ratio, Gross Profit Margin

c.

Exchange variable: Exchange AMEX NYSE OTC

d.

Frequency 5 3 17 25

Percent Frequency (5/25) 20% (3/25) 12% (17/25) 68%

Gross Profit Margin variable: Gross Profit Margin 0.0 – 14.9 15.0 – 29.9 30.0 – 44.9 45.0 – 59.9 60.0 – 74.9

Frequency 2 6 8 6 3 1-7

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Cha pt e r1

e.

Sum the Price/Earnings Ratio data for all 25 companies. Sum = 505.4 Average Price/Earnings Ratio = Sum/25 = 505.4/25 = 20.2

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