FinalExamStatforbusinessFall2014Solution (1)

FinalExamStatforbusinessFall2014Solution (1) - ema BUSINESS...

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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 apt-csch 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 man-made 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 5-month moving avers ; e IE1- - - - A w r 2.801 - Mav I_. E 3 2. cs 2. no 1.? '2. 8 1. Compute a 5-month 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. uses-2.3m: +;.uw +13“ + 1-5“ = '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 2-369— Exercise 3. ANOVA (17 points) Spam is the price we pay to easily eonnnunioate using e-mail. 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 mail-9,36 significance level that the differing university communities differ in the amount of spam they receive in their e-mails? 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» .- eCs-sut‘+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 mam-s in the Aana Excel £19319: - vr "mm mm” TECH—'7 QWTWI 1:1.LECI H g . omega-Mu. .31er m. u ‘fLI. MFA“? I'm-.25; ‘5‘. ¢ B$¢g gas-q. ."I “ LL54! 3n j‘ofl rum " .L'a. “huh-L. MI; J‘M. Mph‘l' “M31. wank-l kg QBQL‘Sgég-i. ii “'me in ski} Tun) "AL: 1%: Ithahu‘ . . Airhx... 3...» am: .¢'* 1.. 9,91 EXerciSE 4. Descriptive Statistics (5 points) The data represent the salaries (in thousands of dollars) ofa sample of 14 employees of a firm: 40.01 29.6 28.2 27.2 26.5 24.8 24.3 23.7 21$ 22.7 21.1 20.4 20.2 11.9 mus m1 "In-It 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 claim-MG” Jim. (4 1-3.3..1" uni-MI. Mal fiuu. Lt Sun-.11”? Ail-lube. Duo 3.1-... at“. 21.1 7.1.: 2.3.: am. uses 26...? if 21.3-+13.t-91.1.-s-+2.H.1+1u.t 4-26.: 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 “ll-i _' 1I(u':..3\ rdt'PCNE'1) r-iw'PCKrfi) -?CK-I3-TCK 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 - O-I‘B‘z— O._3¢5 = 0.5.1.3 tea-s 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) = 'PCKa-l) —'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(x-8 l + PCK no) a 0.0‘4H-io-ITL + eras-1 + 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 half-hour 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 , 4-354- 4- 1.1:. “is COL-ls. nmku poul- 01 234' is?“ a. . W'Qau. = eta: mas... .f as .. at») s m: SIN-H =6.“ Q —n coke-ls MAM-u palm-j 6.1.: 12:6". to, s we.“ _- 29.34:. .911... Jhflwfiw in .m magma. :- reams—zine = 2.3 nutes (u) in a half-hour sitcom : . E"; the value of f is the ween: A4 4L.- m tll. hull-unfl-QI. mun-if Ml... uku— Dnm-L Ain‘t-Julian- “m4.- gfl'ml l1. Matt... 60.40“?- lld- thdllo‘lm gut-M.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 populist-ion variance is [0035; for the population of the radiation levels. Suppose the-sample mean is 415.51. 'J 1 Is it e one-tail or a two-taiI-test'? 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 ell-A pupae-Inha- oulnmm indium ,. we. as... tum-Bud “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‘d-7‘ X-Eg ' =fl2.32' 25+ I “Vim ease/m 1-3.3td-L‘G Merlin) He Inhale-5%. Thus—emu“ is 25!- C '24., also. “in “‘9..th 3) Check on result I: comufin the P-value. Com are with al ha and conclude. ?— Om... e- ‘PCec—zen +‘PC'iL-e-LM.) = .2 [P61 can-2.91.5] =- .2 59.: —1Ceee¢.2..31fl a CD"; - camean a E mot-twig = enact: 3. ufifi“ J I“ Sumo. mac-M . 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 192-271;; {3 Similaremey the " I "" mounts is approximately The accountant prepares inn. ‘- forji-IWhat ia the confidence in ewal‘? Direction.- Round u : to 3 di; its a er the decimal .A-az-IO.BD MI‘O 3 “3:15. Meyer-hm Icar— é a a.e-e.ee [OJ-‘36: ~ ' ‘ Janeen-Immune“: 1&3" a“ *“hhM-P “PC: :1: “Jurahhr —'o 1‘" _ 4.6444 Mr ‘4‘": 4h. a: an: o. MEWS-m. two! I an 5“ 1- 1... JG "Ilh. " '4'6'4" " .. .Ie. 5. g i + q, . cm n “It W P nth, 7.1 2ge-Ims ‘3" :9 s %3+'.6‘t5 V353" We” 204-253. 5. p e mum-i. 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 working-woman given that she has one or more children? that she is either a workin-woman or has no children? ’PCeu'fi) nu)»: rca) -’PCtenfi) .-:.- GAG—+03% —o..44 =05: 4 Are the events ‘Workin-Woman“ 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 film-l BM Mimic-Put“. 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 viii-1:! iier ii-Iiil‘iilniifir‘? 2' Note that in this table, the come "," means "." the decimal dot. Table 1. Excel ee_reetmhotr Le" T‘_'f_;.:f_:e:_.-. We: . t-0 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: pv-fl- UK I- 1-3-Dll-43CIS-i3 = 44.192. ‘11”!— el‘nlr Squib-I. -e.'..._-.. ..{m-tu'» Jill: '3 I, Qua-a... - 14.49 12 b. If the Ian; of a Iar amour]: base can ; '3 .. omit-Is)— l-Ma 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“ emu-Q with M 4m». ;-1 ‘ I ‘l - is the alternative hypothesis? 1’C-‘kg41d03 max-d I Gus-0.1- =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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