Final_Exam_cheat_sheet_-_ECMB12H3_Stats_-_Apr_19_2010

Final_Exam_cheat_sheet_-_ECMB12H3_Stats_-_Apr_19_2010 -...

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Unformatted text preview: Alandmnsaanpleisdmmfi'rmamrmalpepflatiaawi‘mmemer andslaiidarli deviation rr=i. A 95 percenr :mfidmce iarerral fan: is. [29.9. 393-). lt'the sample data are used to rest 3:131:39 versus H_:,u:—39.1l:ue smallest signifiraarelerelthatfig Iarilllierejertledierasesttt: I"‘. I r I I .I J. I ' ' I “ll. I I. 'j‘lnr'll 1": .li. .-. "P All - '.'-.«‘...i" e " '2: .'~ --g. :."I|. ".I ' '\-. J _ n; ._ ~ «g; I' “- “ -,'-_ r. ._;.l. ‘_.'_.,,- 2: kn 'I .'\'-' - _. . _ .- -I __;. Fr z: .u L!- - _‘ L. I); 1 .: I - 1.- - .. a. - _-— . I'd-[F1 — r.- 4-. .‘_r 3' 'l. _.I_-.|..-__ IL {1 II '-' y 'I'J' ~.LF him. II—lw; ~ n , :tr- .I he _ ' ' 7 i ;,.'-_ «‘- .. ' - — .- i'l "-; _ . ' L " .— -__I. V I._I_.__I_I . _ \ Ix. ' ' -."'.‘ Anrdsmsample .IL.X;......I5 is selected fi'ama mrmalpap‘ulatianwtlhmem _ E _ ,er aadetandardderiasim rr.Ler I berhesamplemeanand ELL—I]: =129. M For Ir-Irhat talJE set" E u'illthe hyp-aliiesis Hn:,.'.r=19 he arrayed atthe 5"!"- levelafsigaifiraiire'.‘ §_Jl-_._‘,:.r.l- ..=_\I .L-I -_.;-._-_ “' '_—'|_5' 'LI._=[- ,'.J _1 J-l“-:(-1.I":J-':-'-'- 9. Tlell-llillxirh lt-J'."J_ Tic-{i I " 'l' J'- " 'l L1! H l 1 7 fl” i—‘m . Lawn-Mun *- . . '_| . ' ' ' -_ L. .I 5 9: —‘:'_~.;_?~- ..—l'2~‘ 7.3+ flu _ x: '1}_" _- ~_— I' < {e 4- ~_ " Ll —~.tu.-- l l” ".91. - - - ' .1”? ' -1:“ 1! 7- am ~. —— Mug-1.- »ib T;- -'—'."’-.'.’l 5- «J. iI-1ull‘l'fi. Ban-7m“: (March 39. I992} rep-urned the perrent changes in mains ms'eetraent marlaets aimmd Lhewarlli. The variame L'll'll‘JE perceatretnrnsmrera 1-minth penis-dams 49. A sample at 24 markets dur'ragthe first 3 moirth af1992 shsa'ed asample sarianreiirttiepercemrermasmbefilti. Tatarifttevariaacein peroenrrenuasfartiie incesunenrmarkereappeaistahase iraeasedia taint} malts act'199l.thetla}aeaf1l:netfiretalistirie mean]: w - eT ‘ «'3 - 4.,“ L1": 993 It; _ .1: L- : -.;' lyE __ 4-1 2-3.? . l_ . I; 2 4.; .. . . . I.) .I LII? 31 7 It“? Farh'ag Fan-raw (lamaq‘ I939} repeated an a survey of salary iiifm'rnat'um far mtnataiierfafaccmadaas. Twatndepealienrsamplfishawedflre fallaatngresaltsaneunylevfl salarifi: Public humming Eganuims Sample size 19 15 Kean 123559 311.999 Standard DEL-jam “.199 51.999 AssameLhaten‘h'ylevel salaries fella-er approximatetfamaldisrritmim. Tn tatii'thesrandarli detrialiaasafentijrlerelsalarifiarethesamemeUh-lic Assamesefiiaasmdflaramdms.1l:etalueafdietestsrafieficisdasestta |..-.- - Letfl bethemeanafamdsmsmipleafsizelmfiamapapulafimuithmem l9aads|a1a1ardaemtimIELEhe1temeaaafanrdamsampleafsimlfl9 Eramapapulafinawiflimeaniflandsraaflarddatatian 5. Amethatfi and Ema Map-ardent. Thepnhabilitf Pfi—Efiflisflnsestm _ 'z -_ ‘- ~i1. "‘ " l'u'.-mk-‘. _- an; _‘_____._ .llm! -.. “In; . _.1 _ x . _N at. \.— M. __"'_- ',"- :_I. _ k. .- _J_-(\ H, '.‘-'. ~ s: —‘.- ll,L ll-Ta. __. - -I __ - ___..__ I. .. '7 Let?beflremeanafaiandamsampleafsiae4fiamamaldism'badanuirh mean 19aad51aadard|ietiafianl fhedremeanafamdamsmleacfsiae4 Eramammaldisu'fli‘ufianuirhmm 3 mismdarlidfi'iafiml lt'Lhetr-m samples-are independent. fliepu'ababiliry if] is flaseetm me arm. an}. .mmqi nut ll“: cm iflwl'ihlrll. Pfiszi} mn- 113M911“ wit-17m) *‘l‘jwis..§+-fi ) “ll-#4 =9 v"; l 7.. 1199-19 £1 For the pair of naeasuremerits—{xlhtfllrLygl....I:xm.}'fl} the least squares reyfis'baullineafyaaxie Iii-3Landthatatfranyis The carelaliml betwemxadyis _ 1'1 _ '4 r— h. .1. r-lfit L. b." r= = a: w. J'=£§ lnaregsasianamalfsis. Lhealimatedsimpleregressianliae is 53-1u—x. The samle mean aflt'is 5-4. Thesample tar-inure air is I and the sample tariarxeaflvis4. mm'matmm' eregesmnliireafraalvis b.=-i= egg-.- J-r 31:3: EH: fi-znlbl! 1.; ff all: 4?: h I" 9-- f‘—- 95'- = “2;, 1m” rig-9:11.: - 92s} =1 :-. .gll=-'|-J;Ij. P; Stair-use test sutures em; a animal distribution with mean ,u and slasutard deriatinnl9.1'hehfpathesambetesbedarefln:p-fl9 and Hamid-9.151. 111mmsampleafsizeISisselernedaadlilesamplemeanisdeaaredhyE. ‘iiiithliledeeisianmleinquestiaa l1.t.he prahatcilh'fafa'l‘fpellemrwten .u-llfi isrlaseetm PHan ll Emu“; ;_[._3:55i'l.? Plat LE ‘3 : 'J-Jllgltfi A managemaatrecruherwmera estimate asimple linear betweenflnnmberaffem an ajab}aa|1 T{salarf}i11habe1mana.gement A Masaryk aflflabsenlalians givesthefiallalingeampmerprim-aut Variable CaeEt' SE at Caefi' Craislam T5 l9.:'- The rueffinimaflieterminatian F'I is flnseatm -' r .:.-1 ._ :.'_;r'.; MI! \:-l:- a ' :11 1:3 2‘1' ‘ | _ .;.-r x _‘I 3 U 'I I _ : I. 3...— Ta restithema-de] is significant. 'llcuel-T etalistil: iecbasarta ._ r-| Last year. a 95"!- rnafilienre immIal far the prep-mien of “HE-a T119 were satisfied with Lhe Mayer's perfumamze I:Iras rep-erred as [99593. 9.3393). This. fail a 959'. ramfilietxe interval fiarthe same paapmim was rep-urned as [DE-'96. 99394). Birth imermlswerebasedaaraamaa empleeafmm. Pmride a 95‘}; :aaiirleare interval for the diffierease l.'|1 pamlaliaan prap-uniaas. Sulmiaam: Ler pl =1ast1feas's popularim paup-arfim p3: Lhie year's pupulaiimpaapirfimn r r _| r r M. 1919': 9.310.-) Lulu-.1] — 91:2 9 — =9.IE—9.9:t:1.9 ’13" ‘1'». a. sea + 4m = — U.1:|:1.9|'5Il|2|.|125l = 4.1: new. in (—0.149. 41a: I) At significance level 995. test the h'prI'JJEiS if there has been a signifisant tmprwemem in dieh'laiazr's salist'arliaan wings. Pmride an approximate p—tlalae fmtiie rest. 3mm: Let p. =lflEt‘fEilJ'5 papalalimpmpunim p2: Lhie year's populalim paaprrlinn H03FI_P: =9. R. rim—p: <9 At 9.95 sigiifisanre let-ill. reject En if 2 s —I.IS45 and arrept Ha if 2 2:- —1.fi45. The rest statisril: is _ R-P: —_eE+H:E=W— ' Z—mumfl' EIHEE 493—409 J13). _+— 1i kfl' E? z: “3:” 11=Uté:-1'4g=—3.gsmeuameerejem |iIJ.flS"9.I' — — ' ' 1‘ ll JlmHWI region. Reject HF and :ansbxietlaat there has been. a signifiraat irate-arm in the Majar' e salisfirlixm ratings. 1mm=fi2 6. 4.953 which is Less than um Ahemartse sohitina: Similarm part (aJ. Leif anng hethemeauandt'arianreofamndomsampleofsizefi froma populationdiarislirrmalwifiimeanfiandsmdarddeuiation 1'3. Itiswell known on: I and 53 are independent. Find the poobabilir'f 110 cf: 6. 5F..‘-fll£-: #:1513195: semen-fies. 55.?ola-:s=-:151.T292'| " _ o—s fistula-24:. [ii—1155': 151529214} _ o—s I, I—3 I, Jilin-$25 Etc-'33 ‘Iosi‘ss' 1o1 ' er= |o= (,- =P|—1.Sc:2'-:l.5. 13.941343 -: fuss-115': =P{—l.5 -: z -: 1.53elj1134343 -: I: -: 36.415] = (0.4312 — o.43_11:-:o.95— M5) = (I. lF'QT-‘fld InvestoosashabomdiereladonstdpherweenrertnnsonmwsnnenlsmCmada and on investmeols oceiseas. The following stunmary slows the annual returns iinperteniagej ooi Canadaand overseas stocks fioo'amnd-ocm sampleod'12 years. —Ceaoada_|;nrerseas_ Hean Ill 12 a i in . . .l i The correlation coefficient between the retuous on Canada and Overseas is I215. Ifaretomonincesuneurinianadaislwhatisdieesfimatedremrnon incfionentoceiseas'.’ Soluliooi: Let Ibe'ltereunmonmt'esttnentotrerseaejitetteretinmooiint'esuneni inCanada 4:: r1.”|rw “EMS 35" I29 auda- E of 12 horror 3 - E~3£)|-k-‘1.3.;- I. - — - — - ’- r. Estimated I—cr+hX—3+III.QI ... At.H.theesiimatedrertn'nomincEunmtomseasis 1' -3+|ZI.9|:D']—1I.I Lfaremrn on int'esunenr fl'l'fl-o-Efli is 5'. what is the Elimaredrerorn on int'esunent in Canada? _ _ Soluliou: Let T he theretorn onintesuneor iii-Canada .l'hetloe rettlrn on mt'esunent overseas. a REL] [o 5135'- U4 and n' 'r—ef 1o—o 4:115 4* 13;, ' .35 ' ' ' " "5 r. Estimared 1'- u+hX- 5.2+fl.4.l.' A ALH. theesiimated rertn'non incmonmtm-Canadais T - 5.2+ Chill:qu -ll.ll An advertising firm bflieues that 2|}; ofthe people have been esposed to a particoJaIa-irertisemeor. Suppose the firm selects a random sample of25{lll people and finds that 55D of memhatreheeuetposeduo the adverlisement. Setup tire nullandalrematitre hypotheses to test ii'tiiere are Ell-I: of the people exposed to the ads-moment. Stateypurcondusionusingtne decision rule a - I295. Ham —fl.2. Hague-I112 Thedecisionruleis n-IIIJZIi. That is. reject Hg. if E -: —1.9IS or 2' 51.96: attept Hg if —1.§'|§ E 31.96. I. _ ... _ p—EQ _ {1.22—02 _1 m “gm”: E z ,n'pme'n in: oer-25m ' Sinredoe teststatisiixZ=25 is grenterfloan 1.96. wereject Hg. and toneludetioat the pnppoo'fioolofpeople estposedro doe adrenisemem is no'tED‘ki. Assume that 2W. of the people hare heen etposed to their advertisement. Snpposediefirmselectsanodimnndomsample of ll'ifllllpeoplewhat isthe prohahilitythatmoredian281l of'lhem hateheenetposedto meadt'ertisemeut’.’ HI .‘1 Solulion: Let _o be Iiiesampleprop-orlion «. q. I’- r. 2% '- .-'t '- :- . — :- [118 . _ P PI? 1604]).- j“IfFl J.- I'J.1ll. — 0.20 P"? :- I- Ii'pq.-ae Ii'-Eo.1to.af..-I-soo_ PIE 2- —"-'I = DST-'2 Assume that ill"?- of the people hate heen etposed to their advertisement. Snpposethefirmwishm mselectmotherlargenndomsnnple ofpeople. This time the firm 'il'iSllE to ensure a prohahiliry of I195 'Ihatover ISE-Lof'doe people in the sample have been erg-used to the advertisement. How many people shruld he selected in dais sample? Soluliooi: Let _a; he the sample pmportiooa The firm wishes to ensure HEoUJEI—flifi. Therefiore r . p—p . ole—om -’ .—o.o1J"'. - . ,.— _ .._ - . —o.os..r -oes Pl.llpq."u 1|I-JZLHIZIlLI-‘u '.~ '14 ' F El metheZ-oahle. —o.u:‘+’fi - 4.545. 1'? - 32.9.m re - 32.91 -1os2.4l Sinrea musthe aninteget. the answeris a=lllllll. Layoct'E and imemploj-‘menr hat-e afiected a suhstantial number of workers in retetoyears. Asmd'fcollected da‘laon t'ariahlm thatmayherelaredtothe number of weeks a Wiring worker has heed jobless. The dependent 1:aiialzule in the study (I'E'I'EEESJ eras defined as the number ofweelts a worker has been jobless due to layofi'. The independent wriahles in the study were as follows: AGE Age ocftioe woo'ker EDUC Numher ofyears of education ELUJJED equalsuo 1 if married ll otherwise llEAJJI equalstolifheadod'hmrseholdlloflim-wise TEN'L'RE Fumherofyears onthejoh HGT equals 1 Lfmanagement oncopatiou. {I otherwise SALES equal 1 ifle occupalinn. U otherwise Amolfipleregressionnmdelhosedonamndoonsmnpleocffifllaypfi'woflers showsRE-I'ilflandthefiollo'n'ingstatisiifi: elem sinefitieut 5mm Consmnr 1D 2 AGE 2|] 5 EDUC -l|lI 4 leLAJLFJED 25 I'll lEIEAJIl 2|] 1'1] TEN'IEE 1|ZI ll HGT 3.5 2.5 SALES I5.5 3.5 Fto'ttennooe. the sample variance of I55 talculaoedas 2W. Tar the overall significance of the nullliple regessinn nor-dd using a 5“."- sigoifirante level. [You mosterrloe deem the null and alternative hypotheses. the decisionrole. devalue ofthe test sadistic mddie tonelusionj Soluiion; Themallaud alternative hypotheses are Hggfij —fi2—,33—fi4—,35—,S¢—,&7—fl {Le..modmisn-orsiguifi.caurj H1:Notall fir—EI. i—I.1.....". ii.e..mnd.elissigni.ficam‘] For Foes. reject 3.} if F:: 224 and accept Hg if F 1124. where F has q'.’ =('.-'.-’12). F_rr—l—.I'r e3 _ so—1—r or A I—K- T l—Iil.ll Reject Hg andtonflndethatthenmdelissiguifitant. What is the estimated multiple regression equa1ion for marriedmmerler areheads of hawseholds'? Seldom; Y = 1-3 — Ioege— IDEDUC — 25 '1 — ED‘I — 1D'1‘ENURE — S.5HGT—d.SSALES = 55 + soege — IUEDUC — lo'rEN'U'BE— S.5‘MGT— o. 53.3.1533 Perform slalistiral rest-.to independeurtariahlfi thatare significaur in predictingthenumlzer of weeks aworlter has heenjohless due to layme Usea 5°."- signit'ttanrelecel. Solulion: Hp :fij -III. fingers-Ill; .I'-12.....l Foo a-=III.I'.'I5. reject HI] if r :- 2.0‘21 oo: .r -: —2.III21: areepr ED 51' —2.Il21'i.r '32.".121'. where rhas eff—'42. {The .r-t-alue with @512 is not available in the gicenrahle. Wehaveused'doe r-tahleerithquI-{I here] —2-1- whichfiallsintherejecdamregjm Predicooo: lLueflicient Standard Boon-realistic Cousaur 1|ZI 2 S AGE 20 5 4- EDUC -I|.'.I I1- -].5 AL'UUUED 25 1G 2.5 HEAD 2U 1U 2J2 TENLEE 10 S 1.25 HGT 3.5 2.5 3.4 SALES 5.5 1.5 LS5? aring the rejecciml regime. to the I—EEI'PJE'E variables AGE. EDL'C. MARRIED. ao1d MGT are variables HEAD. TENL'RE. and SALES are notsigoiiicmt. If a simple regrmsion analysis is perfonned erth AGE as the only independent 1:arialztle. theSun-r qugnm'etifirw{SS£'ju is terire as large as the SE inthe ahove unflliple regression model. Test if this simple regessinn model is or not. using a 5‘3; significanre lewd. Solnlieoi: In diemoltipleregressiooimodelll: - or and r? - uariy'l— 2m. we have 53:" - [a 41.33 - [ejujeooj - oer-o 5m — alssr— {omen-o] — mo srr - rsr—sse - Iroo Lu simple regression with AGE as the only variable. 551E =lll2ll. HEl'IE the ANGVA rah-1e fiorthis simpleregressionis as or H'S r Regression soon 1 5m .11 um 292D 4e 31 some? Total new 4;:- For Foes. reject ere if r :: 4.o4 and actept Hg if F 14-34. where F has q'; = (I. 43}. The talculatedF—statistit inthe ANO‘EA table is Tl. which fills inthe rejection region. The simple regression nude] with AGE as the independent t'ariahle is 5fl-Ell- Alumnad methods: 3- -os FE i' F _ [:1 4H _ [serum l—a- I—oa I ' I 0:. c—1I|['“I'2-§.Ir —Jfi—s.4~oss. with the rejetdon region .r:-:.ol1 or __r" r <:—:.o11-. where rhas cred. For the pair of measurement ':I1.I1u'1:l.|:I:.}':‘l...,':rm_}'fl:l the least squares -."2 which Eallsintherejection region. n M 1 regl'fisionltoeod'yooiris 3.1%. H211.» —I92.S.findti:e1:alue oEExf. ' I-l I-l .. -" r 1 smeelt'—3.weha1.redfl-III anddl—E .1- 1 1 n I. 1 .1- l .1- Exr—— Tag. — 19:.a—— Ex. 435.5" Ex. .I- J'rfj ,-' 2“..:.1 , I i“Jul , M Tharefiora fix} -3351: |- A:Er|alnjnbiscomp1!nadlnLhJeestspsinsariEs.Thammmdstmdard mmmmtntmhmeanhstapmgiwnbdm. 5 Men in hams StandardDwiatiun inhmus I 1 D2 2 I [H _3++—fl2— Assumnomal dist-mm nulinlispmflmt SEEPE. Tmhsiapenmemflnmsmplasnresflenad. EsLh any]! size i515. Fluiiflle paubabfliyintiedjfia’emebmmmmgamsmcmlfletfisjnhm mamasamplesismerfljhms. _ _ fliintLHTbEmEtimsm-mmple‘mmajub. FhsTfindLhEmmmfitminntaui ii] Sulmjmifl It bemafimatomnpletastap I. I: beflnaljmenu Emlsbestepl and .153 heme IZiJDE'III caplet! step 1 I]. 13 m1 1'3 are MEI. LEI-.I1+I:+I3 temmnammmple‘refimjub. E'III':I-£I:I]+.I3+I31-3+I+4-S Fm-{Ij- Farl[.1'1+.I3 +.1:3]— -:1.31+I:I.I3+-:1.2I — My Hamil" follows a nmmaldiscrlhltiun nth mam Hand s'arimeflflfl _ Le‘r I bathe magedmemmmplemmajubinfllefirstsmnple. and 1' baths mgethnsm mmplehs'lhajob Lute second sample. T and f are 'Lnliepemiem. Walla-me T fiaflmannrmaldism‘bufinnmmsm S and-Immune . 1 ammsldisuitmfimuflmmflmdnflsmefl. Hence 3—? fullmisn 25 S—fl-IZI aI':s1'I.ItLrian.:3\sE+E-fl __ _ _ 2s 2s :5 PIE—fl:-ail—JUL:—I:-a.sl+PLT—I-:—a.s_l " . [Li—III “ —|II.5—l‘.|' - 2. Z I: II J JELlfl-‘E JI+P1_ Jam-'25 -fiZIJ S.$]IS'I+PT,E -: 4.139361— D and '1' follows ...
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This note was uploaded on 10/09/2011 for the course MANAGEMENT MGTB03H3 taught by Professor Liangchen during the Summer '09 term at University of Toronto- Toronto.

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Final_Exam_cheat_sheet_-_ECMB12H3_Stats_-_Apr_19_2010 -...

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