cursul 4 - statistica inferentiala

7/30/2019 Cursul 4 - Statistica inferentiala

1/65

]tatlstlma lj`frfjtlaha

Mursuh jr* 5


2/65

Elstrlkutla fgplrlma

Elstrlkutla fgplrlmaelstrlkutla eatfhor gasuratffxpfrlgfjtah

Akatfrfa stajeare fstf ogsur a varlaklhltll saurspjelrll `ata ef mfjtru aeatfhor `ata ef gfelf*

[fiuha fgplrlma2 eatfhfsf aproxlgfaza mu

elstrlkutla jorgaha eama2

03& elj eatf sujt ljtrf 1 sl 1 s*


3/65

Vj stuefjt sf ljtfrfsfaza ef elstrlkula pujmtabfhor ha fxagfj eup mf aoktljut 39 elj 1>>* A a`hat ma elstrlkula pujmtabfhor sf aproxlgfazamu `orga ef mhopot( mu gfela 96 l akatfrfa stajeare ef 1>* ]fmojstata ma stuefjtuh a huat uj pujmtab gal garf efmat gfela( ear jusf stlf mat ef kuj fstf pujmtabuh*

]f aphlma rfiuha fgplrlm2

03& elj stuefjtl au pujmtabuh ljtrf 06 sl 36*


4/65

Uforfga hlglt mfjtrah

]f mojslefr uj fajtloj ahfatorlu `orgat elj j varlaklhfhfahfatoarf2 S1( S;( ***( Sj4

Slau amffal elstrlkulf ef prokaklhltl l sujt rfmlpromljefpfjefjtf*

Gfela fajtlojuhul fstf o varlaklh ahfatoarf*Mf `ujmlf ef elstrlkulf a prokaklhltlhor l morfspujef gfelflfajtlojuhul?

^fjtru a rspujef ha amfast jtrfkarf( sf f`fmtufaz urgtoruhfxpfrlgfjt2

]f arujm ef jorl zarurlhf l sf eftfrglj gfela arujmarlhor4 sfmrfaz @E^ pfjtru el`frltf vahorl ahf hul j*

x


5/65


j 7 =>

j 7 1j 7 ;

j 7 1>


6/65


Mojmhuzll fxpfrlgfjt2Mu mrfstfrfa hul g2

Gfela rgjf amffal* Akatfrfa stajeare sf rfeumf*

@E^ a xsf aproplf ef elstrlkula jorgah*

Uforfga hlglt mfjtrahEam S1( S;( ***( Sjaparlj ujul fajtloj ahfatorlu prfhfvat eljtr'

o popuhalf mu gfela l akatfrfa stajeare l j fstf

su`umufjt ef garf atujml2

x jx

=* Elstrlkula gfelfl x fstf aproxlgatlv jorgah

1* ;*


7/65


Eam sf mogklj mfhf trfl oksfrvall jtr'o sljiur `orguh sfokljf2 rfprfzljt elstrlkula jorgah stajeare*

j

x

R /

R rfprfzljt elstrlkula jorgah stajeare*

Amfst rfzuhtat pfrgltf s sf utlhlzfzf gfela fajtlojuhul mafstlgator ah gfelfl popuhalfl *


8/65

Fstlgatorl pujmtuahl

popuhatlf

fsajtloj

]tuelu lj`frfjtlah

1* Elj popuhatlf sf prfhfvfaza uj fsajtloj;* ]f ajahlzfaza fsajtlojuh=* ]f `amf o prfelmtlf pfjtru popuhatlf pf kaza fsajtlojuhul*5* ]f gasoara bustftfa prfelmtlfl*


9/65

Fstlgatorl pujmtuahl

x

p

fajtloj popuhalf

statlstlm paragftru

gfela akatfrfa stajeare s proportla p

Fstlgarfa pujmtuah ' mfa gal kuj fstlgarf a ujul paragftruah popuhalfl( ear mfh gal prokaklh ju fstf fiah mu paragftruh*


10/65

Ljtfrvahuh ef fstlgarf

Ljtfrvahuh ef fstlgarf ' ljtfrvah ef vahorl marf ljmhuef vahoarfaparagftruhul popuhalfl*

Eam ljtfrvahuh ef fstlgarf fstf slgftrlm( elstajta ef ha

fstlgatoruh pujmtuah ha gariljfa ljtfrvahuh ef fstlgarf sfjugfstf garb ef froarf*


11/65


Garla vrfa s'l vje masa l arf jfvolf ef vahoarfa ef pla amasfl*^opuhala ' masfhf slglharf elj martlfr*

Aifjtuh lgoklhlar ahfif ma fajtloj( masfhf slglharf elj martlfr

marf s'au vjeut j uhtlgfhf asf hujl sl apol hf abustfazprfurlhf ef vjzarf pfjtru a ljf sfaga ef el`frfjfhf eljtrfmasa Garlfl l masfhf vjeutf

5;>*>>> 55>*>>> 59>*>>>

5=>*>>> 56>*>>> 59>*>>>

5=>*>>> 50>*>>> 53>*>>>

Fsajtloj prfturl abustatf ef masf

Aifjt lgoklhlarmahmuhfaz gfela

fajtlojuhul l o rfmogaje mavahoarfa ef pla a masfl ef 56>*>>>eoharl*

Aifjtuh lgoklhlara `muto lj`frfja vahorll gfell a popuhalfl*


12/65


Gfela popuhalflfstf( prokaklh( ljtrf 5;6*>>>% l 596*>>>%(Garba ef froarffstf ef ;6*>>>% `a ef fstlgarfa ljllah ef56>*>>>%* Fstlgarfa fstf2 56>*>>>% ;6*>>>%

Garba ef froarf;6*>>>%

Fstlgator pujmtuah56>*>>>%

Ljtfrvahuh ef fstlgarf5;6*>>>% ' 596*>>>%


13/65

Ljtfrvahf ef jmrfefrf

Ljtfrvah ef jmrfefrf ' ljtfrvahuh a marul prokaklhltatf ef amojljf vahoarfa aefvrat a paragftruhul popuhalfl fstfmujosmut

Ljtfrvahuh ef jmrfefrf pfjtrugfela popuhalfl eam2 akatfrfa stajeare a popuhalfl fstf mujosmut( j fstf su`lmlfjt ef garf pfjtru a utlhlza ujmla R ha mahmuhuh

vahorlhor mrltlmf ahf ljtfrvahuhul ef ljmrfefrf*

jRx

jlvfh efjmrfefrf

R vahoarfmrltlm

& 1(056


14/65

Arla 7 jlvfhuhef ljmrfefrf



15/65

Fxfgphu2Efmajuh vrfa s fstlgfzf jugruh gfelu ef orf pfsptgja humratf ef stuefjl* Vj fajtloj ef 5< efstuefjl humrfaza lj gfelf ;5 orf( mu o akatfrf stajeare ef5 orf* Fstlgatoruh pujmtuah2 gfela fajtlojuhul 7 ;5 c*

Marf fstf ljtfrvahuh ef jmrfefrf pfjtru uj jlvfh ef jmrfefrfef


16/65

Eama jlvfhuh ef jmrfefrf mrftf( mrftf l garba ef froarf*Ef fxfgphu( eam mrftf jlvfhuh ef jmrfefrf mrfstf ha &( fstf

lgposlklh ef rfahlzat `r a `amf rfmfjsgjtuh jtrfill popuhall*


17/65


Gfela popuhalflfstfma o osifat marfjtotefauja atljifmfjtruh takfhfl ef Earts

Ljtfrvahuh ef jmrfefrffstf spatluh efsmrls ef ljta j glmarfpfjtru a prljef sifata lj mfjtru*


18/65

Ljtfrvah ef jmrfefrf pfjtru Ljtfrvah ef jmrfefrf pfjtru maje sfmujoastf akatfrfa

stajeare a fsajtlojuhul sf mahmuhfaza mu elstrlkutla t ]tuefjt2

j

stxm

mu j '1 iraef ef hlkfrtatf

Fxfgphu]ahhy aparljfa ujfl oriajlzall ef sajatatlf #O],( marf a avutratljiuh ef 0;* ]ahhy a trfmut ha o jou O]* ^fjtru a fvahua

ratljiuh gfelu ah joll O]( ;> ef gfgkrl au `ost mcfstlojal l arfzuhtat uj ratlji gfelu ef 06( mu o akatfrf stajeare ef 1>*Marf fstf ljtfrvahuh ef jmrfefrf mu uj jlvfh ef jmrfefrf ef


19/65

003(506;>

1>>


20/65

Ljtfrvah ef jmrfefrf pfjtru p

Lj elstrlkula kljoglaha( p fstf proporla ef summfsf apopuhalfl*

j pramtlm( sf utlhlzfaza statlstlmlhf fajtlojuhul pfjtru a fstlgaproporla popuhalfl p*

^roporla fajtlojuhul ef elgfjslujf j fstf fstlgatoruhpujmtuah pfjtru p*Elj tforfga hlgltfl mfjtrahf( eam jp : 6l j#1'p, : 6( elstrlkula

proporlfl fajtlojuhul arf o elstrlkulf aproxlgatlv jorgah*

j

pp

pp

1

p

Ljtfrvah ef jmrfefrf pfjtru proporla popuhalfl( p*

j

ppRp

j

ppRp

11


21/65

Fxfgphu;>> ef o`frl elj Mahlòrjla au òst ljmhul jtr'uj fajtloj ahfatorlu l s'

a efsmopfrlt m ;6 eljtrf fl au vorklt ha tfhfòjuh goklh( `r cajes'`rff* ] sf mahmuhfzf fstlgatoruh pujmtuah ah proporlfl efmojeumtorl auto marf utlhlzfaz tfhfòajfhf goklhf lhfiah l s sf

mojstrulasm ljtfrvah ef jmrfefrf pfjtru 7 >(1;6 sau 1;(6&

^fjtru uj jlvfh ef jmrfefrf ef (>1;6(>;>>

1;6(>11;6(>690(;1;6(>

Garba ef froarf pfjtru sojeab fstf ef 0&( l sf a`lrga mu o jmrfefrfef


22/65

Fstlgatoruh pujmtuah pfjtru ^fjtru a fstlga varlala sau vohatlhltatfa ujul sft ef eatf(

sf utlhlzfaz akatfrfa stajeare(s ma fstlgatorpujmtuah ah akatfrll stajeare a popuhalfl *

FxfgphuLjvfstlllhf A l K au rata rfjtaklhltll ef 0& pf aj* Lj

uhtlgfhf ;5 ef hujl( ljvfstlla A a avut akatfrfa stajearea fajtlojuhul ef =& pf huj( j tlgp mf pfjtru ljvfstltlaK( akatfrfa stajeare a fajtlojuhul a `ost ef 6& pfhuj* ]f poatf a`lrga m ljvfstlla K fstf gal vohatlh lgal rlsmajt efmt ljvfstlla A elj mauza vahorll gal garla akatfrll stajeare fstlgatf*

^fjtru a mrfa uj ljtfrvah ef jmrfefrf pfjtru fstlgarfaakatfrll stajeare( sf utlhlzfaza elstrlkula ;*


23/65

Ljtfrvahuh ef jmrfefrf ;Ljtfrvahuh ef jmrfefrf ju fstf slgftrlm efoarfmf elstrlkula ;

fstf aslgftrlm*

;

;

;

; 1(

1

H[

sjsj

Arla 7jlvfhuh ef

ljmrfefrf

Arla 7 jlvfhuhef ljmrfefrf

Ljtfrvahuh ef ljmrfefrf2


24/65

Fxfgphuj gsurarfa pfr`orgajfl ljvfstllhor( akatfrfa stajeare fstf o

gsur a vohatlhltll sau a rlsmuhul* Eouzfml ef rajeagfjtfhujarf ahf ujul `oje gutuah ljelm uj rajeagfjt gfelu hujar

ef 1& l o akatfrf stajeare a fajtlojuhul ef 6&* ] sfmahmuhfzf ljtfrvahuh ef jmrfefrf morfspujztor jlvfhuhul efjmrfefrf ef '1 7 1< iraef ef hlkfrtatf


25/65

]f poatf spujf mu jmrfefrfa ef


26/65

Ufstarfa lpotfzfhor ujfl popuhall

]tatlstlma lj`frfjlah sf utlhlzfaz2

pfjtru a fstlga uj paragftru ah popuhalfl l a gsura

`laklhltatfa fstlgrll pf uj ljtfrvah ef jmrfefrf*

ha tfstarfa ujfl lpotfzf mu prlvlrf ha uj paragftru ahpopuhalfl( aphlmalf marf mojstltulf fhfgfjtuh mfjtrah ahgftoefl tlljl`lmf ef mfrmftarf*


27/65

@orguharfa prokhfgfhorifjfrahf ahf mfrmftarll

@orguharfa lpotfzfhorsl prolfmtarfa

fxpfrlgfjtuhul

@orguharfamojmhuzllhor lj hlgkabjfstatlstlm

Mohfmtarfa sl ajahlzaeatfhor fxpfrlgfjtahf



28/65

@orguharfa jtrfkrlhor ifjfrahf efmfrmftarf

Mfhf gal guhtf jtrfkrl porjfsm ef ha o surs ef ljsplralf sauo leff efsprf suklfmtuh sau `fjogfjuh ef ljtfrfs*

Mtfva fxfgphf ef jtrfkrl ifjfrahf2

]jtatf2 ^oatf uj slstfg pukhlm ef jirlblrf ah sajatatf s`lf gal f`lmlfjt efmt slstfguh prlvat ef asliurrl?

Gujm2Marf fstf f`fmtuh lgliralfl lhfiahf l fxtfrjahlzarfahomurlhor ef gujm asupra ratfl ogabuhul*?

Fmojoglf2Fstf pamcftuh ef stlguharf fmojoglm ahiuvfrjuhul f`lmlfjt j elgljuarfa rfmfslujll? Feumalf2 Fstf prfa smugp ljvatagajtuh ujlvfrsltar pfjtru

stuefjll?


29/65

Lpotfzfhf sujt efmharatll efsprf paragftrl popuhalfl* Mtfvafxfgphf2

Mfh pulj ;>& elj lj`ramtorll gljorl sujt prljl l mojeagjal

p : >(; Pfjltuh gfelu hujar ah aksohvfjlhor ef `amuhtatf fstf ef mfhputlj 6>> furo : 6>>

^ujmtabuh gfelu ah irupfl 1 fstf amfhasl mu ah irupfl ;1 7 ; ^romfjtuh kohjavlhor ef majmfr puhgojar elj @rajta fstf galglm efmt efmat mfh elj Ahkajla p1 8 p; Akatfrfa stajeare a kursfl ef vahorl elj Jfw \ord fstf mu ef

1> & gal garf lj amft aj : 1>



30/65

Ufstarfa lpotfzfhorfstf o promfeur( kazat pf fvlefjf ahffajtlojuhul l pf tforla prokaklhltll( pfjtru a eftfrglja eamlpotfza 2

fstf o efmharalf rfzojaklh l ju trfkulf rfspljs(

fstf jfrfzojaklh l trfkulf rfspljs*Lpotfza tfstat sf jugftf lpotfza juh( C>* Eam lpotfza juh fstf

jfrfzojaklha sf tfstfaza lpotfza ahtfrjatlva( Ca

Lpotfza juh( C>2 efmharalf mu prlvlrf ha vahoarfa ujul paragftru

ah popuhalfl( marf sf prfsupujf aefvratpfjtru smopuh tfstrll* Lpotfza ahtfrjatlv( Ca2 efmharalf mu prlvlrf ha vahoarfa ujulparagftru ah popuhalfl marf sf prfsupujf aefvrat( eamlpotfza juh fstf rfspljs prlj tfstarf*



31/65

Oksfrvatll2

1* Lpotfza ahtfrjatlv mojtrazlmf j goe jfmfsar lpotfzajuh4 agkfhf lpotfzf ju pot `l aefvratf j amfhal tlgp*

;* Lpotfzfhf trfkulf s `lf efmharall efsprf paragftrlpopuhalfl( l efsprf statlstlmlhf fajtlojuhul*

=* Lpotfza juh tfstfaza fiahltatfa #7( ( ,( lar lpotfza

ahtfrjatlv ljfiahltatf #8* :( ,*

5* ^rlj tfstarf sf jmfarm ma lpotfza juh s sfrfspljif l s sf suslj lpotfza ahtfrjatlv*



32/65

Fxfgphf ef lpotfzf juhf sl ahtfrjatlvf2

C>2 p >(;> Ca2 p : >(;> C>2 6>>> Ca2 : 6>>> C>2 1 7 ; Ca2 1 ;

C>2 p1 p; Ca2 p1 8 p; C>2 1> Ca2 : 1>



33/65

^fjtru a tfsta o lpotfza fstf jfmfsar uj goefh statlstlm marf efsmrlfmogportagfjtuh eatfhor l paragftruh popuhalfl marf fstf tfstat*

Goefhf statlstlmf sujt elj `aglhla jorgah( mfhf gal lgportajtfelstrlkull sujt2 ; R( U sl @*

@lfmarf goefh sf `orguhfaz pf kaza ujor lpotfzf a mror oportujltatfsf vfrl`lma*

Ef fxfgphu2 guhtf goefhf mojslefr m gfela fajtlojuhul arf oelstrlkulf aproxlgatlv jorgah( lpotfz marf ju sf aphlma eamsfturlhf ef eatf sujt glml sau elstrlkultf aslgftrlm*

]f ahfif uj tfst statlstlm marf fstf utlhlzat pfjtru a efmlef eam lpotfzajuh sf rfspljif sau ju sf rfspljif*



34/65

@orguharfa lpotfzfhor

Lpotfza juh Lpotfza ahtfrjatlv

Eftfrgljarfa goefhuhul aefmvat

Ufst statlstlm Ufstarfa ljtfrvahuhul mu ujasau eoua hlgltf

]taklhlrfa mrltfrlhor ef efmlzll

Jlvfhuh ef sfgjl`lmalf l putfrfa tfstuhul



35/65

Frorl j huarfa efmlzllhor

Huarfa ujfl efmlzll lgphlma o prokaklhltatf ef a àmf o ahfifrf irflt*

Ufstarfa lpotfzfhor mfrf2 s sf rfsplji lpotfza juhl s sf suslj lpotfza ahtfrjatlv s ju sf rfsplji lpotfza juh*

]f pot àmf eou tlpurl ef frorl2 Froarf ef tlp L sf rfspljif lpotfza juha mje amfasta fstf

aefvrat* Froarf ef tlp LL ju sf rfspljif lpotfza juha mje amfsta fstf

àhs*

Ha tfstarfa lpotfzfhor( sf la j mojslefrarf prokaklhltatfa ef a àmf ujaelj amfstf frorl


36/65

C>fstf ammfptat C>fstf rfspljsC>fstf aefvarat Efmlzlf morfmta Froarf ef tlp L

C>fstf `ahs Froarf ef tlp LL Efmlzlf morfmta

Frorl j huarfa efmlzllhor


37/65

Fxfgphu ef froarf ef tlp L

O mogpajlf ef gfelmagljtf mogfrmlahlzfaz uj slrop( marf s'a eovfelta `l ljf`lmlfjt j tratagfjtuh tusfl* jaljtf ef mogfrmlahlzarf(mogpajla a mfrmftat l staklhlt m gfelmagfjtuh fstf f`lmlfjt jtratagfjtuh tusfl( mffa mf jsfagj s'a rfspljs lpotfza juh mslropuh ju arf jlml uj f`fmt asupra kohll*

O mogpajlf marf tfsta utlhlzarfa Ljtfr`frojuhul ha tratagfjtuh ujfl kohlpuhgojarf( a akajeojat mfrmftarfa mje tfstarfa a artat mLjtfr`frojuh fstf ljf`lmlfjt* Mogpajla ju a rfult s rfspljilpotfza juh m gfelmagfjtuh fstf ljf`lmlfjt* Mf sf jtgpheam gfelmagfjtuh ar `l òst mu aefvrat f`lmlfjt? Eam mogpajlaàmf froarf ef tlp LL? ôslklh( ear elj gogfjt mf gfelmagfjtuh ju a

òst mogfrmlahlzat( ju sf mujoatf aefvruh*

^rokaklhltatfa gaxlg ef a àmf o froarf ef tlp Lsf jugftf jlvfhef sfgjl`lmalf ah tfstuhull sf jotfaz mu *

^rokaklhltatfa ef a àmf o froarf ef tlp LL sf jotfaz mu *


38/65

Pahoarfa mrltlm l zoja ef rfspljifrf

Eama jlvfhuh ef sfgjl`lmatlf ah tfstuhul fstf ahfas( sfeftfrglja elj `ujmla ef elstrlkulf ef prokaklhltatf atfstuhul statlstlm o zoj j marf lpotfza juh fstfrfspljs ' zoj ef rfspljif

Pahoarfa mrltlm ' hlglta eljtrf zoja ef rfspljifrf l efjfrfspljifrf*

^fjtru o sltualf eat( fxlst o vahoarf mrltlm l o zoj efrfspljifrf*

]upra`aa totah a zojfl ef rfspljifrf fstf fiah mujlvfhuhul ef sfgjl`lmalf *


39/65

Pahoarf mrltlma

]f rfspljif C>Ju sf rfspljif C>

Arla zojfl efrfspljifrf 7

Arla zojfl lj marfju sf rfspljif 7 1'

>

Ufstarfa ujlhatfraha a lpotfzfl

Vj tfst fstf ujlhatfrah

eam lpotfza ahtfrjatlv(Ca( a`lrg o sltuatlf( mugar `l2C>2 Pfjltuh gfelu ah`fgflhor fstf mu mfh ah

krkalhor*Ca2 Pfjltuh gfelu ah`fgflhor : efmtkrkalhor*

Efoarfmf fiahltatfa fstfspfml`lm lpotfzfl juhf(lpotfza ahtfrjatlv vaeftfrglja marf gariljfa ljtfrvahuhul sf va tfsta*


40/65

>

Arla zojfl efrfspljifrf 7 /;Arla zojfl effspljifrf 7 /;

Pahoarf mrltlmaPahoarf mrltlma

]f rfspljif C>]f rfspljif C>

Ju sf rfspljif C>

Arla zojfl lj marfju sf rfspljif 7 1'

Ufstarfa klhatfraha a lpotfzfl

Vj tfst fstf klhatfraheama lpotfzfl ahtfrjatlvfCa ju a`lrga o sltuatlf(mug ar `l2

C>

2 Pfjltuh gfelu ah`fgflhor fstf fiah mumfh ah krkalhor*Ca2 Pfjltuh gfelu ah`fgflhor ju fstf fiahmu vfjltuh gfelu ah

krkalhor*

j tfstuh klhatfrah( sfgpartf j eou prl(efoarfmf fxlst eou

zojf ef rfspljifrf*


41/65

Fxfgphf ef tfstarf a gfelf `a ef o vahoarfprfsupus >2

Ca2 : >tfstuh gfelfl pfjtru hlglta supfrloarl fstf efjuglt tfstuh hlgltfl elj erfpta*

Ca2 8 >tfstuh gfelfl pfjtru hlglta lj`frloar l

fstf efjuglt tfstuh hlgltfl elj stjia*

Ca2 >tfstuh gfelfl pfjtru agkfhf hlgltf*



42/65

Mohfmtarfa l ajahlza eatfhorfxpfrlgfjtahf

Mohfmtarfa sl vfrl`lmarfa eatfhor

F`fmtuarfa fxpfrlgfjtuhul Pfrl`lmarfa vahorlhor akfrajtf

]taklhlrfa tfstuhul statlstlm l /sau vahoarfa hul p

Mogpararf mu vahorlhf mrltlmf Mogpararf mu

]f la o efmlzlf pfjtru C>

[fspljifrfa C>sl susljfrfa Ca Ju sf rfspljifC>


43/65

Uratarfa vahorlhor akfrajtf

O vahoarf akfrajt fstf eata marf el`fr `oartf guht efmfhfhahtf eatf elj sft*

Pahorlhf akfrajtf pot `l eftfrgljarf ef2

irffhl ha jrfilstrarfa eatfhor( eatf marf ju am partf elj popuhalf( fvfjlgfjtf rarf rfahf*

FxfgphuPjzrlhf trlgfstrlahf ef masf a 1> aifjl sujt2 ;( ;( =( 5( 6(

6( 0( 0( 9( 6>


44/65

Mu vahorl akfrajtf @r vahorl akfrajtf

Gfela > 5(55

Gfelaja 6(>> 6(>>

Akatfrfa stajeare 15(61 1(31

Ha mahmuharfa statlstlmlhor( sf oksfrv m gfela l akatfrfa stajearesujt a`fmtatf ef vahoarfa akfrajt( j tlgp mf gfelajaju sf smclgk*

O sohulf pfjtru popuhala mu vahorlhf fxtrfgf fstf utlhlzarfa statlstlmlllj`frfjlahf*

Elairaga Kox sf utlhlzfaz pfjtru a eftfrgljarfa vahorlhor akfrajtf*

Uratarfa vahorlhor akfrajtf


45/65

Hoilma tfstarll lpotfzfhor

Ha tfstarfa lpotfzfhor sf la efmlzla eff rfspljif sau ef jfrfspljifrf alpotfzfl juhf* ^romfsuh efmlzlojah slglhar mu mfh elj gatfgatlm ef +aeovfel prlj mojtraelmlf fstf2

]f prfsupujf m C>fstf aefvrat l Cafstf mogphfgfjtar hul C>* ]f ajahlzfaz eam eatfhf morfspuje mu C>

Eam eatfhf ju morfspuje( sf eovfeftf m C>fstf `ahs2 sfrfspljif C>l sf propujf Ca ' efmharalf putfrjlm*

Eam ajahlza eatfhor ju fstf mojmhuefjt pfjtru rfspljifrfa C>sf a`lrg m eatfhf sujt jfmojmhuefjtf ' efmharala shaka*

Oksfrvatlf2

1* Efmharatlf shaka ' ju s'a efgojstrat C>( eoar a `ost lj`lrgata*;* Lj statlstlm a efgojstra o lpotfza jsfagj m lpotfza fstf

susljut mu mfrtltueljfa ef #1',1>>&*


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Fxfgphu

Vj mfrmfttor eorftf s sutlja a`lrgala m( j gfelf( stuefjtll trlglt galguht ef 1>>> ef ]G]'url pf huj*

Lpotfzfhf ef mfrmftarf sujt2

C>2 7 1>>> vs Ca2 : 1>>>*

Efmlzla prlj marf C>fstf rfspljs2 jugruh gfelu ef ]G] trlglsf efstuefjl efpftf 1>>>*

Efmlzla prlj marf C>ju fstf rfspljs2 ju fxlst eovfzl su`lmlfjtfpfjtru a susljf a`lrgala m jugruh gfelu ef ]G]'url trlglsf ef

stuefjl efpftf 1>>>*

Oksfrvatlf2Efmlzla sf hlgltfaz ha popuhala elj marf s'a prfhfvatfajtlojuh


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Mogparfa vahorll p mu Ufst statlstlm ' vahoarf mahmuhat elj eatf j moj`orgltatf mu

goefhuh statlstlm ah eatfhor*

]f mahmuhfaza vahoarfa mrltlm p pfjtru jlvfhuh efsfgjl`lmalf ahfs( *

Ufstuh statlstlm sf mogpar mu vahoarfa mrltlm a tfstuhullpotfzfl*

Eam vahoarfa p 8 ( C>fstf rfspljs Eam vahoarfa p : ( C>ju fstf rfspljs*


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Pahoarf mrltlma


Ufststatlstlm

Efmlzla ef rfspljifrfa a C>

C>2 7 1>Ca2 : 1>

]f ahfif sl sf mahmuhfaza

vahoarfa mrltlm p 7 tfststatlstlm*

Ufstuh statlstlm sf jmaerfazj zoja ef rfspljifrf2 p 8

Efmlzlf ' sf rfspljif C>*

Efmharalf putfrjlm2 Eatfhfsuslj lpotfza ahtfrjatlv*


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Pahoarf mrltlma


Efmlzlf ' ju sf rfspljif C>

C>2 7 1>Ca2 : 1>

]f ahfif sl sf mahmuhfazavahoarfa mrltlm p 7 tfststatlstlm**

Ufstuh statlstlm ju sfjmaerfaz j zoja efrfspljifrf2 p :

Efmlzlf ju sf rfspljif C>*

Efmharalf shak2 Eatfhf sujtjfmojmhuefjtf l ju sprlblj

lpotfza ahtfrjatlv*


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Ufst ah vahorll gfell vs vahoarfa lpotftlmFxfgphu2 O mogpajlf ef proeusf ahlgfjtarf aphlm pohltlma j marf

mojljutuh efmharat ah ujul proeus fstf lefjtlm mu ah proeusuhulàkrlmat*

Ljtrfkarf2 Irfutatfa efmharat a proeusuhul morfspujef mu irfutatfarfah?

Vj statlstlmlaj j mojtrohuh mahltll efmlef s tfstfzf stlmha mu sos ef solaef 10 ujmll* Lj amfst sfjs prolfmtfaz fxpfrlgfjtuh*

]tatlstlmlajuh fstf autorlzat sa prfhfvfzf =0 ef stlmhf tlgp ef o ora( ef hao sljiura gaslja ef lgkutfhlat4 elj eatf ajtfrloarf 7 >(6 oz*

]f tfstfaza gfela popuhalfl vs vahoarfa lpotftlm ef 10 ujmll*

]f ahfif uj tfst mu eou hlgltrl( efoarfmf mogpajla fstf prfomupatatt supraugphfrfa mt l ef sukugphfrfa stlmhfhor*

Lpotfzf ef mfrmftarf2C>2 7 10 ' gaslja ef ugphfrf ùjmlojfaz morfmt

Ca2 10 ' gaslja ef ugphfrf ju ùjmlojfaz morfmt*


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Efoarfmf fstf mujosmut tfstuh statlstlm fstf2

Ufst ah vahorll gfell vs vahoarfa lpotftlm

Goefhuh sf aphlma eama elgfjslujfa fajtlojuhul asliur elstrlkulajorgah a gfelfl fajtlojuhul*Froarfa ef tlp L ' sf rfspljif lpotfza juh l sf a`lrga m gaslja eflgkutfhlat ju `ujmlojfaz morfmt atujml mje fa `ujmlojfaz morfmt*jtrumt somlftatfa ju vrfa s sf oprfasm ljutlh proeumla l s

rfmahlkrfzf gaslja( statlstlmlajuh ahfif s hlgltfzf prokaklhltatfa frorllef tlp L prlj staklhlrfa ha 6&*

]tatlstlmlajuh a prfhfvat =0 ef stlmhf ef sos ef sola elj marf o sljiurvahoarf fstf jfokljult ef 19(60 ujmll* Pahoarfa fstf ammfptat j sftuhef eatf*

j

xR

/


52/65

]f mahmuhfaz vahoarfa gfelf a fajtlojuhul l a tfstuhul statlstlm*

55(1=0>(6/

10'10(1;R1;(10 ujmllx

Gfeoea 12 Lpotfza juh sf rfspljif eama R fstf j zoja ef rfspljifrf('1*


53/65

Pahoarf mrltlmaPahoarfmrltlma ]f rfspljif C>]f rfspljif C> Ju sf rfspljif C>

Gftoea R



54/65

p


Gftoea p


55/65

Mojmhuzllhf l rfmogajearlhf statlstlmlajuhul pfjtrumojeumfrfa mogpajlfl2

+Ju fxlst eovfzl su`lmlfjtf pfjtru a mojmhuzloja mgalja marf ugphf stlmhf ef sos sola ef 10 ujmll`ujmlojfaz jfmorfspujztor* Amfast mojmhuzlf sfkazfaz pf gsurtorl f`fmtuatf pf =0 ef stlmhf pf eurataujfl sljiurf orf ef proeumlf*

P rfmogaje gojltorlzarfa mojtlju a galjll pfel`frltf smclgkurl( efoarfmf fstf poslklh o froarf ugaj

j aparlla varlallhor ef irfutatf*+



56/65

Froarf ef tlp LL l putfrfa statlstlm

j fxfgphuh ajtfrlor( statlstlmlajuh ju a rfult s rfsplji lpotfza juh(efoarfmf prokaklhltatfa ef a àmf frorl ef tlp L #ef rfspljifrf a ujfllpotfza juh aefvrat, a efplt jlvfhuh ef sfgjl`lmalf ef 6&*

]tatlstlmlajuh ar `l putut àmf o froarf ef tlp LL( eama galja ùjmlojajfmorfspujztor*

Vja elj sarmljlh fstf ef a ajahlza prokaklhltatfa ef a àmf froarfa eftlp LL ' *

' prokaklhltatfa ma s ju `lf rfspljs lpotfza juh eam fstf àhs

]tatlstlmlfjl utlhlzfaz putfrfa statlstlm( marf fstf mogphfgfjtuh hul *


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Lpotfz

Lporfza juh Lpotfza ahtfrjatlv

Eftfrgljarfa goefhuhul morfspujztor

Ufst statlstlm Hlgltarf ujl sau klhatfraha

Mrltfrll pfjtru huarfa efmlzlhor

Jlvfhuh ef sfgjl`lmalf l ajahlza putfrll



58/65

Ju sf rfspljif C> ]f rfspljif C

>

C>fstf aefvrat 1' Froarf ef tlp L

C>fstf àhs Froarf ef tlp LL

1'putfrf


Eam tfstuh lpotfzfl arf putfrf glm( fstf el`lmlh s sf rfsplji C>( mclaream C>fstf àhs4 mfrmftarfa ar `l o plfrefrf ef tlgp sl kajl*

j fxfgphuh ajtfrlor( lpotfza ahtfrjatlva òst m 10 ujmll( aelmgalja ugphf stlmhfhf a 7 10*>>>1 ujmll( lar Cafstf pramtlm aefvrat*Eam sf ajahlzfaz putfrf l froarfa ef tlp LL sf ahfif o vahoarf pfjtrugfela popuhalfl pfjtru lpotfza ahtfrjatlv #a,( marf fstf +pramtlm el`frlt+ef gfela lpotfzfl juhf #>,*

Amfast el`frfj pramtlm sf jugftf elgfjslujfa f`fmtuhul*


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El`frfjaeljtrf gfellhf lpotfzfhor sf jugftfelgfjslujfa f`fmtuhul

>2 vahoarfa gfelfl a popuhalfl pfjtru lpotfza juh a2 vahoarfa gfelfl a popuhalfl pfjtru lpotfza

ahtfrjatlv Elgfjslujfa f`fmtuhul2 +el`frfj pramtlm+ jtrf >l a

7 |> ' a|*



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] prfsupujfg m sf f`fmtufaz uj tfst ujlhatfrah ah gfelflpopuhalfl2

C>2 7 > Ca2 : >

]f lau j mojslefrarf mfhf eou ira`lmf2

Ira`lmuh ef sus fstf elstrlkula gfelfl fajtlojuhul pfjtrulpotfza juh* Roja elj erfapta a vahorll mrltlmf fstf zojaef rfspljifrf*

Ira`lmuh ef bos fstf elstrlkula gfelfl fajtlojuhul pfjtrulpotfza ahtfrjatlv pfjtru vahoarfa spfml`lm a a* ^famfst ira`lm sf poatf gasura slputfrfa tfstuhul


Pahoarf mrltlma


61/65

Pahoarf mrltlma


fstf asomlata muprokaklhltatfa frorll ef tlp L(sf rfspljif C> maje fstfaefvarata

fstf asomlata muprokaklhltatfa frorllef tlp LL( ju sfrfspljif C> maje fstfàhsa

ûtfrfa fstfasomlata mu

prokaklhltatfa ef arfspljif lpotfza C>àhsa


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Gftoef ef mrftfrf a putfrll statlstlmf

Goeahltl ef mrftfrf a putfrll [fahlzarf

Mrftfrfa elgfjslujll fajtlojuhul Mrftf mostuh l sf rfeumfvarlaklhltatfa eatfhor

Mrftfrfa jlvfhuhul efsfgjl`lmalf( Mrftf prokaklhltatfa ef rfspljifrfa lpotfzfl C>aefvratf froarf eftlp L

Ahfifrfa vahorll a el`frlt ef > [fzuhtatfhf pot `l gal puljsfgjl`lmatlvf

[fef`ljlrfa popuhalfl pfjtru aglmora akatfrfa stajeare

[fzuhtatfhf pot `l prfa hlgltatf

]f rfmogaje f`fmtuarfa ujultfst ujlhatfrah l ju klhatfrah

^ot proeumf rfzuhtatf prtljltoarf

F h t t t h l


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Fxfgphu putfrfa tfstuhul

^hmufhf ef `rj ahf autokuzfhor sujt prolfmtatf s eurfzf jgfelf( mfh pulj 0>*>>> ef dg l o mogpajlf vrfa s tfstfzfamfast a`lrgalf*

Mogpajla ef autokuzf vrfa s eftfrgljf vahoarf +pramtlm+ musmopuh ef grlrll sliuraja autokuzuh( efoarfmf uhtlgfhf

tagpojrl s'au proeus ha mfh pulj 63(>>> dg* Eam akatfrfastajeare fstf ef 6*>>>( lar elgfjslujfa fajtlojuhul ef 6>(marf fstf putfrfa tfstuhul eam gfela pramtlma fstf ef 63(>>>dg* #sf prfsupujf 7 >*>6,

]f eftfrglja vahoarfa mrltlm a tfstuhul* C>sf rfspljif eam R 8 '1*056 ]f mahmuhfaza vahoarfa marf morfspujef vahorll mrltlmf2

6333=96>/6>>>056(10>>>>>

j

Rx

x

F h h l


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C>sf rfspljif eam 8 633=9]f mahmuhfaza prokaklhltatfa ef rfspljifrf a C>( eam Ca fstf

aefvrat2

x

331(>13(16>/6>>>63>>>633=9

/

633=9

633=9>

R^R^jR^x^

^utfrfa amfstul tfst fstf ef 33& l fstf ef 1;&*

Pahorl ljllahf

> 7 0>*>>> dga 7 63*>>> dg 7 >(>6j 7 6>

7 6>>> dg

Pahorl mahmuhatfF`fmtuh grlgll 7 ;*>>> dgPahoarfa mrltlm 7 63*3=9 dg 7 >(11 sau 1;&^utfrfa 7 >*331> sau 33&

Fxfgphu2 putfrfa tfstuhul


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^utfrfa 7 33&

Pahoarf mrltlma

]f rfspljif C> Ju sf rfspljif C>

cursul 4 - statistica inferentiala

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