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Unformatted text preview: ' ema BUSINESS SCHOOL 2014/2015 Academic Your
Fall session EAI Program Statistics for Business BUS 2702
a CREDITS COURSE INSTRUCTORS: Pierre Aboussouon
Audrey Dolmosso
COURSE COORDINATOR: Audrey Dolmosso FINAL EXAM Extrait du Reglemeut lutérieur du SKEMA Business School
Chapitre VI  Frantic Ies etudisnts devront a'ahstenir dc quittet' la sells. ti'exameu. saut‘ cos grave
lurs des examons sent iutcrdites. Article In ; Durant tt‘iute aptcsch écrite.
Article 21 : Les communications outra etudiauts
Article 23 : 23.1  La simple possession d'uu document non autorise eoustutee uu coul‘s d'uue epreuve eerite ou I‘utilisatiou do papier uuue quc
eelui distributi pour l'épreuve d'eitmnen sera consideree couuuc une teutetivo dc frauds. I 23.3  Tottte frauds eamctdriseo eutt'elnera l'cXclusiou immediate dc l'etudiaot de la saile tl'exaiuen. Article 24 : Tout etudinnt ayant commie unc hands on uue tentative dc ﬁ‘audc dilmcnt constatée pounra tetre tmtluit en Conseil Llc
‘ Discipline. letluel s coittpetcnco pour prendre toute decision d‘eseiuaion tetttporuire no deﬁnitive de l'Ecole. Lu et upprouve
; Signature do l'étudient: v        I I I I III  v v       I  v . . . . . . . . . . . . .. Academic Regulations of SKEMA Business School Chapter VI  Cheating Article Ztl : During exams. students are not allowed to exit the t'tmm. except in case tif‘errtergeney‘ Article 21 : it is strictly prohibited to communicate with any other student during the exam. ‘ Article 23 : 23.1 n it is strictly prohibited during exams to possess any document or to use material or paper which has not been espresst
authorised. 23.3  Any student Found in breach of these rules will be immediately expelled from the exam room. Article 24 : Any student found guilty of cheating or trying to cheat will be presented In the Academic Committee whose sanction may
be as high as exclusion oftheschooi. Read and AppruVed ‘ Student‘s signature : ........ .. o n  s y . . . . . . . Ill t . v . . . u t . l . . . . . . DIRECTIONS: in Please, write clearly. The use of a pencil (crayon a popier) is highly recommended.
a Answer on this exam paper and inside the dedicated areas. : Please, do not unstaple pages.
If those first three con i ions re ot fulfilled at east 4 oin s could he re oved.  Drafts or other paper sheets will not be graded. Les feuiﬂes de brouiilon ou autres ne seronr pas nurses.
I A correct answer with no explanation may not get full credit but a wrong answer with Intermediate
steps (method or calculation) may get partial credit. I The use of non—programmable calculators is allowed.  Students are not permitted to share a calculator.
105 : aims possible Exercise 1. Poisson Probability Distribuﬁon . (6 points)
During the ﬁshing months, a marina at a large manmade reservoir noted that boats were arriving at the average of evoryﬁﬂ to use the boat ramp. Let x be the number of boats arriving during the small
Direction: Round up raidigﬂ's oﬁer the decimal point. PCK 51.3  “MK and arcs: an +?CK'1)
“m 1 .:4 I ‘i _g.‘
e... .36 45.516 4,. ol 1! '.
0.993%  0.09:? i QOS'ao 2) ;_ .4 o.a6a8 — owns
: 0.369: Exercise 2. Time Series Analysis (5 points)
Here are data on the monthly price of gas, which is a ccmpcnent of the Consumer Price Index (CPI).
The CPI represents changes in prices of all goods and services purchased for ccnsumpticn by urban
hetISeholds. The data table shows the ﬁrst months of year 2006. mm 5month moving avers ; e
IE1 


A w r 2.801 
Mav I_.
E
3 2. cs 2. no 1.?
'2. 8
1. Compute a 5month moving average of the ﬁrst months of 2006. Fill in the previeus table. Round to 3 digits after the decimal point U
Show ur co  taticn for the ﬁrst value. uses2.3m: +;.uw +13“ + 15“ = 'Eg‘ = M's: I—
E. 2. Use it to redict the value for Setember 2006. J usti .
3. are + 343% + 1.563 + 2.531. +1.3el
S = Jesse
: r 2369— Exercise 3. ANOVA (17 points)
Spam is the price we pay to easily eonnnunioate using email. Does spam affect everyone equally? In a
preliminary study, university professors, administrators, and students were randomly sampled. Each
person was asked to count the number of spam messages received that day. The results follow. Can we
infer at mail9,36 signiﬁcance level that the differing university communities differ in the amount of spam
they receive in their emails? Direction: Round up to 2 dt' « 'ts 0 er the decimal mm. 5 Professor and
Students —
.
hm 2. The following tables are Excel screenshots but information are missing. Complete the cells shaded in
grey of the following tables. Explain your computations below. Round to 3 digits qﬂer the decimal point when it is necessary. Anova: Single Factor V SUMMARY Grou 5 Count Sum Average Variance
Professor and Students 6 42 _ 48,8 LIL" an
Administrators 42 10,5 21,667 __
——_— 8" as.» ANOVA ' . Source of Variation
Between Groups
Wlthln Groups Total 334,4 9 09. as» . eCssut‘+s(m.e.R.a\‘ 1: 23M ﬁSA aﬁﬁ i =3; Tn 75h»: I BE! l
1130.) 3. DD 011 ra'cct Ho? State wh 01' wk not. 0.“! A 44.26
ﬂ.“ d Tug" i," 4. [nte ret this result. Docs sam affect eve . one: euall ? f
5. James F. wants to veﬁfy those results and gum yhosa mams in the Aana Excel £19319:
 vr "mm mm” TECH—'7 QWTWI 1:1.LECI
H g . omegaMu. .31er m. u ‘fLI. MFA“? I'm.25; ‘5‘. ¢ B$¢g gasq. ."I
“ LL54! 3n j‘oﬂ rum " .L'a. “huhL. MI; J‘M. Mph‘l' “M31. wankl kg QBQL‘Sgégi. ii
“'me in ski} Tun) "AL: 1%: Ithahu‘ . . Airhx... 3...» am: .¢'* 1.. 9,91 EXerciSE 4. Descriptive Statistics (5 points) The data represent the salaries (in thousands of dollars) ofa sample of 14 employees of a firm:
40.01 29.6 28.2 27.2 26.5 24.8 24.3 23.7 21$ 22.7 21.1 20.4 20.2 11.9 mus m1 "InIt 14.: 21.n “2.1.: 13.1 tu me a“ 13.1—29.1. '13.:
9.. Calculate the median sal . ‘ ha.“ b. Com ute the 28.57296 trimamd mean.
newsman '2 1+
LOO claimMG” Jim. (4 13.3..1" uniMI. Mal ﬁuu. Lt Sun.11”? Aillube. Duo 3.1... at“. 21.1 7.1.: 2.3.: am. uses 26...?
if 21.3+13.t91.1.s+2.H.1+1u.t 426.: Mr: M. Inﬂ 11.5119]. = 6 Exercise 5. Normal Distribution (4 points)
'1' he amount of time spent by American adults playing sports per week is normally distn'butecl with e meat:
of :5 @ﬁmaﬂd standard .  . * .41»? I holtrs. «Find the probability that a randomly selected Aiiierican adiiltpiays Sport ' n " er week. Justify. p H I!
 1.1 ._ ’P(2.s¢.e¢. 9.5:) _ ?(2.Lu¢'e an) +’?(o ca (9.5:) i I_ O. "'\' 0.33': Olgz'a'} "" “m u" if Exercise 6. Binomial Probabilities (8 points)
A state senator believes that 'ﬁlieﬂhﬁiof all senators on the Finance Committee will Strongly support the tax
proposal the wishes to advance. X is the number of senators who strongly support the proposal and X is a binomial variable. Round up to three digiiS aﬂor the decimal point. Justtﬁ). 1. Suppose that this belief is correct and that 5 agitators are approached at random. Calculate the following
probabilities, using either the binomial formula or the binomial cumulative table (Appendix 2).
What is the robabili that'_'_"i5fthe,1' will stronl an out the roosal? 'Blu “lli _'
1I(u':..3\ rdt'PCNE'1) riw'PCKrﬁ) ?CKI3TCK III)4“ ‘3) .. gig—J .o.3‘_.n_——" on" 1"  I" .e .1’ —"_ .3‘.‘
'4 a“: 4.th @ ) Mat, D Ira )3!!! J = A  moot' "' (3.010  OI‘B‘z— O._3¢5 = 0.5.1.3 teas 1,00,} .4 — ‘PCK 5.1.3: 4 oaaa . meat b What is the rohabili exactl 2 senators will strap an art the mesa]? ch .. n = _=_!_.. mlcm . em
a! a! ﬂ on 'Pera) = 'PCKal) —'l’(x.s\') a: mu— 6.133! 2. Suppose that this belief is correct and that itsepators are approached at random. What is the probability that at least 4. of . e 9 will strongly support the proposal?
Use the Bloom] distribution table A endix .3 . 150‘ at.) . 1’(xsu) +90: air) +P(xes\+rar .o) +‘P(x8 l + PCK no)
a 0.0‘4HioITL + eras1 + one: hour: 4 clone = 0.336 Exercise 7. Descriptive Statistics and Hypothesis Testing (13 points)
[a your favorite TV program often interrupted by advertising? CNBC presented statistics on the average
number of" programming minutes in a halfhour sitcom. The following data (in minutes) are representative
ofit's ﬁnding: 20.02 21.06 21.52 21.66 22.37 23.36 23.82
Assume the population is approximately normal. Ie mean round :1 to 2 di  rs aﬁer the decimal ‘ ii ‘20.:‘2 + 1A. as +2.1.n. + 11.6 + 11.3: 4 1.3.3: + 1.3.3:.
I.“ I. a Calculate the sam .ﬁsthh 4 Sta : am .Hme ,
4354 4 1.1:. “is COLls. nmku poul 01 234' is?“
a. . W'Qau. = eta: mas... .f as .. at») s m:
SINH =6.“ Q —n cokels MAMu palmj 6.1.: 12:6". to, s we.“ _ 29.34:.
.911... Jhﬂwﬁw in .m magma. : reams—zine = 2.3 nutes (u) in a halfhour sitcom
: . E"; the value of f is the ween: A4 4L. m tll. hullunﬂQI. munif Ml...
uku— DnmL Ain‘tJulian “m4.
gﬂ'ml l1. Matt... 60.40“? lld thdllo‘lm gutM.th
d4... tude— More. Mnmﬁ 'l'lu. duh. 4iva 1i“...
i no  amm . ' . m \I' Hail—“l4 2J8! an
Exercise 8. Hypothesis Testing (8 points)
An experimenter is interested on the hypothesis, testing problem:
Ha : p = 420 versus H]: it #3420 ‘ where n is the average radiation level in a research laboratory. Suppose that a sample of n = 2? radiation
level measurement is obtained and the experimenter wishes to use a value of the populistion variance is [0035;
for the population of the radiation levels. Suppose thesample mean is 415.51. 'J
1 Is it e onetail or a twotaiItest'? 5+1! I. 'l‘ulv H "H 2 Does the ex erimenter eeeet the null h I; othesis with a s1» iﬁeenee level = 5%? “I ellA pupaeInha oulnmm indium ,. we. as... tumBud “l”. “L
Druid I... THEADD —II ru=dlw I{n 1m, eeetuhj e e.:— EED.: em: a one: “inel In}; :4."5 null  Edict. I‘d7‘ XEg ' =ﬂ2.32'
25+ I “Vim ease/m 13.3tdL‘G Merlin) He Inhale5%. Thus—emu“ is
25! C '24., also. “in “‘9..th 3) Check on result I: comuﬁn the Pvalue. Com are with al ha and conclude. ?— Om... e ‘PCec—zen +‘PC'iLeLM.) = .2 [P61 can2.91.5]
= .2 59.: —1Ceee¢.2..31ﬂ a CD";  camean
a E mottwig = enact: 3. uﬁﬁ“ J I“ Sumo. macM . a .019 H d. O‘D:
(no 1:. 9L
Exercise 9. Conﬁdence interval of the population :0 (8 points) A cost accountant wishes to establish the aVerage meant. 11, spent by executives per day on travel and
lodging. Then a comparison, between the average and the amount tumed in to be reimbursed, will be made
and unreasonably big: o  w expense amounts audited.
A random Sample =2" ‘ = ' e xe'nee ' is taken. The 192271;; {3
Similaremey the " I "" mounts is approximately The accountant prepares inn. ‘ forjiIWhat ia the conﬁdence in ewal‘? Direction. Round u : to 3 di; its a er the decimal .AazIO.BD MI‘O 3 “3:15. Meyerhm Icar— é a a.ee.ee [OJ‘36: ~ ' ‘ JaneenImmune“:
1&3" a“ *“hhMP “PC: :1: “Jurahhr —'o 1‘" _ 4.6444 Mr ‘4‘": 4h. a: an: o. MEWSm. two! I an 5“ 1 1...
JG "Ilh. " '4'6'4"
" .. .Ie. 5. g i + q, . cm
n “It W P nth, 7.1 2geIms ‘3" :9 s %3+'.6‘t5
V353" We” 204253. 5. p e mumi. 10 Exercise 10. Probabilities (10 points)
A surVey of [000 randomly selected married women ShOWBd that 660 of these women time one or more  i , while the rest have no children it?
CH of omen, 360 are working women ( randme selected.
Direction: Round up tﬁdt‘glts after the decima! point. 1) Fill in the following contingency table with probabilities. Justify your computations. 2) What is the probability that this woman is a workingwoman given that she has one or more
children? that she is either a workinwoman or has no children? ’PCeu'ﬁ) nu)»: rca) ’PCtenﬁ)
.:. GAG—+03% —o..44 =05: 4 Are the events ‘WorkinWoman“ and “has one or more Children“ indeendent? Wh or wh not? PCe/M = 0.38 J, 't C e) . 0.3:
taco/Ari 4' 15a.) Eta.13 ﬁlml BM MimicPut“. Exercise 11. Measures of association (12 points)
Table below lists the weight (in pounds) and length (in inches) for l i ,3 bass (Source: The
Mathematics Teacher, [997, p. 666). Let those observations viii1:! iier iiIiil‘iilniiﬁr‘? 2'
Note that in this table, the come "," means "." the decimal dot.
Table 1. Excel ee_reetmhotr Le" T‘_'f_;.:f_:e:_.. We: . t0 1. mama»): wagueomdot m 2) to Using the previous data, find a simple linear regression model for predicting the weight of a
let emouth bass ﬁom knowlede of its le‘n ' . L: pvﬂ UK I 13Dll43CISi3 = 44.192. ‘11”!— el‘nlr SquibI. e.'..._.. ..{mtu'» Jill: '3 I, Quaa...  14.49 12 b. If the Ian; of a Iar amour]: base can ; '3 .. omitIs)— lMa 3) Using Excel command in English, indicate what we need to type up to. compute the population
variance of X. Be recise. .. VnR .‘B( M. I An.) 4) The coefﬁcient of determination is 94.67%. Do you see any problems in using linear relationship as a
model for these data? Iueﬁ . 3H.G‘% 3 3°”
0° WM“. 4. “men an“ emuQ with M 4m». ;1 ‘ I ‘l  is the alternative hypothesis? 1’C‘kg41d03 maxd
I Gus0.1 =Q.Heeu
A.  W .473 Ti c 33 “at. 13) Stage 2. Compute f3. rF, E 1:02 :3. 335.993) = TC?) 1.su)
= 9.5+ 'H—mu can) : c.9382. 3. What happens to the value of [3 as :1 gets smaller? (Note: Do not calculate the new beta [3.) l4 ...
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