estimation and confidence intervals

Tung Nget, MSc 6-1

CMBUkTI 6

bMENgEckénKMrUtagkmμécdnü

sßitiBaNiC¢kmμ

eroberog nigbeRgonedaysa®sþacarü

Tug Eg:tTel: 017 865 064

E-mail: [email protected]: www.nget99.blogspot.com

Tung Nget, MSc 6-2


• vtßúbMNg³ enAeBlEdlGñkbBa©b;enAkñúgCMBUkenH GñknwgGac³

1. eRCIserIsKMrUtagRbU)ab

2. yl;BImUlehtuEdleKEtgEteRbIKMrUtagkñúgkarsikSaGVImYyGMBIsaklsßiti

3. ecHsg;cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIsÁal;KmøatKMrUsaklsßiti

4. ecHsg;cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIminsÁal;KmøatKMrUsaklsßiti

5. cenøaHTukcitþsRmab;smamaRtsaklsßiti

6. ecHsg;cenøaHTukcitþsRmab;smamaRtsaklsßitikñúgkrNIsÁal;KmøatKMrUsaklsßiti

7. ecHsg;cenøaHTukcitþsRmab;smamaRtsaklsßitikñúgkrNIminsÁal;KmøatKMrUsaklsßiti

Tung Nget, MSc 6-3


• vtßúbMNg³ enAeBlEdlGñkbBa©b;enAkñúgCMBUkenH GñknwgGac³

8. KNnatémø Z edaysÁl;cenøaHTukcitþ

9. eRCIserIsTMhMKMrUtagd¾smRsb

10. eRCIserIsTMhMKMrUtagedIm,I)a:n;s μansmamaRtsaklsßiiti

Tung Nget, MSc 6-4


1> viFIeRCIserIsKMrUtagRbU)ab

2> bMENgEckKMrUtagkm μénmFümKMrUtag

3> bMENgEckKMrUtagkm μénsmamaRt

4> témø)a:n;s μanCacMNuc nigcenøaHTukcitþ

4>1> KNnatémø Z edaysÁl;cenøaHTukcitþ

4>2> cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIsÁal;KmøatKMrU saklsßiti

4>3> enøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIminsÁal;KmøatKMrU saklsßiti

4>4> cenøaHTukcitþsRmab;smamaRtsaklsßiti

4>5> kareRCIserIsTMhMKMrUtagd¾smRsb

4>6> eRCIserIsTMhMKMrUtagedIm,I)a:n;s μansmamaRtsaklsßiiti

Tung Nget, MSc 6-5

- dMeNIrkareRCIserIsKMrUtagKWepþateTAelI

karRbmUlRkumtMNagtUcénsaklsßiti.

- KMrUtagEdl)annwgpþl;nUvB½t’manEdlGac

[eKeRbIedIm,IeFVIkar):an;sμanlkçN³énsakl

sßitiTaMgmUl .

1-kareRCIserIsKMrUtagRbU)ab (Selecting the Probability Sample)

• ehtuGVIRtUveFVIKMrUtagkmμécdnü?

1> karsikSaelIsaklsßitiTaMgmUyKWRtUveRbIeBlyURtUveRbIeBlyU

2> ééfføøénkarsikSaelIRKb;FatuTaMgGs;rbs;saklsßitiGaceRcInhYsehtueBkeRcInhYsehtueBk

3> karminGacRtUtBinitkarminGacRtUtBinitüüCak;EsþgCak;EsþgelIRKb;FatuTaMgGs;kñúgsaklsßiti

4> kareFVIetsþxøHGaceFVI[vinasdl;lkçN³FmμCatirbs;saklsßiti

5> lTplKMrUtagKWRKb;RKan;¬GacykCakar)an¦ §

viFIsa®sþKMrUtagmanlkçN³RbU)abEdleKeRbICaerOy²man4KW³• KMrUtagécdnüsamBaØ (Simple Random Sample)

• KMrUtagécdnüCaRbBn½ (Systematic Random Sample)

• KMrUtagécdnüBIRKb;Rkum (Stratified Random Sample)

• KMrUtagécdnüBIRkumécdnümYycMnYn (Cluster Random Sample)

§

Tung Nget, MSc 6-6

dMeNIrkardMeNIrkar³³ dMbUgKNna k = EpñkKt;én N/n .

cMeBaH]sSah_km μ Nitra eyIgKYeRCIserIsbBa¢Ikmμkrral;TI16 (845/52). KMrUtagécdnüsamBaØRtUveRbIkñúgkareRCIserIs

ykeQμaHdMbUg ¬BIkñúgcMenamelxerogTI1eTATI16¦ bnÞab;mk

cUreRCIsykeQμaHrral;TI16 BIbBa¢IbnþbnÞab; rhUtKMrUtagén

kmμkrcMnYn52nak; RtUv)aneRCIserIs.

KMrUtagécdnüsamBaØ nig KMrUtagécdnüCaRbBn½

•• KMrUtagKMrUtagéécdncdnüüsamBasamBa ØØCaKMrUtagécdnüEdlKMrUtag

nImYy²man»kasesμIKña[eKeRCIserIs

ecjBIsaklsßiti.

• KMrUtagécdnüsamBaØEckecjCaBIrKW³

¬1¦ KMrUtagécdnüsamBaØminGaRs½y nig

¬2¦ KMrUtagécdnüsamBaØ GaRs½y.

§

KMrUtagKMrUtagéécdncdnüüCaRbBn CaRbBn CaKMrUtagécdnüEdlmanTMhM nedaydMbUgerobFatuénsaklsßitiEdlman NFatu tamlMdab;NamYy.

- bnÞab;mkeKEcksaklsßitiCa nRkumEdlRkumnImYy²

man k Fatu (k = EpñkKt;én N/n ).

- cMnuccab;epþImedayécdnüRtUv)aneRCIserIs bnÞab;mk

Fatural;TI k RtUv)aneRCIserIsBIsaklsßiti.]TahrN_]TahrN_³³ ]sSah_kmμ Nitra mankmμkrsrub cMnYn 845nak;.

KMrUtagénkmμkrcMnYn52nak; RtUveKeRCIserIsecjBIsakl

sßitienaH. cUrGñkGFib,ayBITegVIenHedIm,I)anKMrUtagmYy

edayeRbIviFIsa®sþKMrUtagécdnüsamBaØ.

dMeNIrkardMeNIrkar³³ eKsresreQ μaHrbs;kmμkrnImYy² dak;elIRkdas

ehIydak;kñúgRbGb;mYy. bnÞab;mkRkLúk[esμIsac;

dMbUgeRCIsykRkdasmYysnøwkBIkñúgRbGb; edayminemIl.

rUceKbnþdMeNIrkarenHrhUtKMrUtagénkm μkrcMnYn52nak;

RtUv)aneRCIserIs.

§

]TahrN_]TahrN_³³ ]sSah_kmμ Nitra mankmμkrsrub cMnYn 845nak;.

KMrUtagénkmμkrcMnYn52nak; RtUveKeRCIserIsecjBIsakl

sßitienaH. cUrGñkGFib,ayBITegVIenHedIm,I)anKMrUtagmYy

edayeRbIviFIsa®sþKMrUtagécdnüCaRbBn. §

Tung Nget, MSc 6-7

KMrUtagécdnüBIRKb;Rkum (Stratified Random Sampling)

KMrUtagKMrUtagéécdncdnüüBIRKb;RkumBIRKb;Rkum³³ dMbUgeKEcksaklsßitiEdlmanTMhM N Ca k Rkumrg ¬dac;KñaBIr²¦ ehIyeKeRCIserIs

KMrUtagBIRKb;RkumnImYy². viFIenHmanRbeyaCn_ enAeBlsaklsßitiGacRtUv)aneKEckCaRkum²c,as;las;

edayEp¥kelIlkçN³rYmNamYy.

]TahrN_]TahrN_³³ ]bmafaeyIgcg;sikSaBIkarcMNayelIkar

pSBVpSayBaNiC¢kmμ cMeBaHRkumh‘unFM²cMnYn352

kñúgshrdæGaemrik edIm,IkMNt;faetIRkumh‘unEdl

mancMNUlRTBüx<s; )ancMNayelIkarpSayBaNi

C¢kmμkñúkarlk;nImYy²eRcInCagRkumh‘unEdlmancM

NUlTab rI»nPaBEdrrWeT.

cUreRCIserIsKMrUtagRkumh‘unTMhM50tamviFIsaRsþ SRS.

edIm,I[R)akdfaKMrUtagKWCatMNagd¾RtwmRtUvrbs;Rkum

h‘unTaMg352/ Rkumh‘unTaMgGs;RtUveKEckCaRkum

tamPaKryéncMNUlRTBü ehIyKMrUtagEdl

smamaRtnwgTMhMeFobénRkumRtUveKeRCIserIs

edayécdnü.

Rkum

PaBcMeNj

¬cMNUlRTBü¦ cMnYnRkumh‘un eRbkg;eFob cMnYnEdlRtUveRCIsCaKMrUtag

1

2

3

4

5

cab;BI 30 % eLIg

20 %-30 % 10 %-20 % 0 %-10 %

»nPaB

8

35

189

115

5

0>02

0>10

0>54

0>33

0>01

1*

5*

27

16

1 srub 352 1>00 50

Tung Nget, MSc 6-8

KMrUtagécdnüBI;RkumécdnümYycMnYn (Cluster Sampling)

KMrUtagKMrUtagéécdncdnüüBIRkummYycMnYnBIRkummYycMnYn³³ dMbUgeKEcksaklsßitiEdlmanTMhM N Ca k RkumrgtamFmμCatiEdlekIteLIg

kñúgEdntMbn; rWtamlkçN³déTeTot. bnÞab;mk RkumTaMgGs;RtUeKeRCIserIsedayécdnü ehIyKMrUtagRtUv

RbmUledayécdnüedaykareRCIserIsecjBIRkumnImYy².

]TahrN_]TahrN_³³ ]bmafaeyIgcg;kMNt;BITsSn³rbs;GñktaMglMenA

kñúg Oregon sþIGMBIeKalneya)aykarBarbrisßan

shBn½ nigrdæ. cUrGñkGFib,ayBITegVI edIm,I)anKMrUtagmYy

edayeRbIviFIsa®sþ KMrUtagécdnüBIRkumécdnümYycMnYn.

Cluster sampling GacRtUv)aneKeRbIedayEckrdæCaÉkta

tUc² ¬tamtMbn; rI extþ¦ rYceKeRCIstMbn;edayécdnü--

]TahrN_ ykbYntMbn;--bnÞab;mkykKMrUtagénGñktaMg

lMenA BIkñúgtMbn;nImYy² kñúgcMeNamtMbn;TaMgenH ehIy

smÖasBYkeK.

cMNaM³ dMeNIrkarEbbenHCabnSMénkareFVIKMrUtagkmμBI

RkumécdnümYycMnYn nigkareFVIKMrUtagkmμécdnügay.

§

Tung Nget, MSc 6-9

2-bMENgEckKMrUtagkm μénmFümKMrUtag (Sampling distribution for the sample means)

bMENgEckKMrUtagkmbMENgEckKMrUtagkm μéμénnmFmFüümKMrUtagmKMrUtagCabMENgEckRbU)ab‘ÍlIetEdlmanral;mFümKMrUtagTaMgGs;rbs;TMhM

KMrUtagEdleK[EdlRtUv)aneRCIsecjBIsaklsßiti.

]TahrN_]TahrN_³³ Rkumh‘un]sSahkm μmYymanbuKÁlikEpñkplitTaMg

Gs;7nak; ¬cat;TukfaCasaklsßiti¦. cMNUlRbcaMem:agrbs;

buKÁliknImYy² RtUveK[kñúgtaragxageRkam.

1> cUrKNnamFümsaklsßiti.

2> cUrrkbMENgEckRbU)abénmFümKMrUtag cMeBaHKMrUtagTMhM2.

3> cUrKNnamFüménbMENgEck.

4> etIeKGacGegáteXIjya:gdUecþcsþIGMBIsaklsßiti nig bMENgEckKMrUtagkm μ.

cMNYlRbcaMem:agbuKÁlik buKÁlik

cMNYlRbcaMem:agKMrUtag KMrUtag

= =

= =

X

$7.00 + $7.50 + ... + $8.5021

$162 $7.7121

;μ

plbkU énmFümKMrUtagTaMgGs;cMnYnKMrUtagsrub

buKÁlik cMNYlRbcaMem:ag buKÁlik cMNYlRbcaMem:ag

2> edIm,IQandl;bMENgKMrUtagénmFüm/ eyIgRtUveRCIserIsKMrUtag TMhM2Edl

GacmanTaMgGs; edaymindak;vijecjBIsaklsßiti bnÞab;mkcUrKNna

mFüménKMrUtagnImYy². manKMrUtagEdlGacmanTaMGs;21.

1> mFümKsaklsßiti Kwesμ I $7.71 EdlrktamrUbmnþ³

3>

( ) ( )nN

N! 7!C 21n! N n ! 2! 7 2 !

= = =− −

Tung Nget, MSc 6-10

2-bMENgEckKMrUtagkm μénmFümKMrUtag ¬RTwsþIbT¦

RTwsþIbT 1 ³ X1,X2,..,Xn CaGefrécdnüenaH 2X , S & S k¾CaGefrécdnüEdr.

RTWsþIbT 2 ³ ebIsaklsßitimanmFüm μ nigva:rüg; 2σ enaHtémøsgÇwmén Xi cMeBaHRKb; i = 1,2,…,n KW³

( ) μ=XE nigva:rüg;én Xi, i = 1 , 2, …n KW ( )i2V X = σ .

RTwsþIbT 3 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØmanTMhM n

ebI ( )E X CatémøsgÇwménmFüm X Edltageday Xμ eK)an ( ) XE X = μ = μ .

RTwsþIbT 4 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØminGaRs½yman TMhM n

ebI ( )V X Cava:rüg;én mFüm X Edltageday 2Xσ eK)an ( )

22XV X

nσ

= σ = .

RTwsþIbT 5 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØGaRs½ymanTMhM n

ebI ( )V X Cava:rüg;én mFüm X Edltageday 2Xσ eK)an ( ) 2

X

2 N nV XN 1n−⎛ ⎞= σ = ⎜ ⎟−⎝ ⎠

σ .

RTwsþIbT 6 ³ ebIsaklsßitimanTMhMGnnþ nigKMrUtagsamBaØGaRs½ymanTMhM n enaHva:rüg;énmFüm X KW nX

22 σσ = .

Tung Nget, MSc 6-11

2-bMENgEckKMrUtagkm μénmFümKMrUtag ¬]TahrN_¦

KNnamFüménsaklsßiti

]TahrN_ 1 ³ ]bmafasaklsßitimYyEdlmanTMhM 5 KW {2,4,11,15,18}.

eKeRCIserIsKMrUtagécdnüsamBaØEdlmanTMhM 2 ecjBIsaklsßitienH.

k- cUrrkbMENgEckRbU)abénmFümKMrUtag X ebIvaCaKMrUtagécdnüsamBaØminGaRs½y.

cUrKNnamFüm nigva:rüg;én X edaypÞal;bnÞab;mkepÞógpÞat;CamYyRTwsþIbT.

x- cUrrkbMENgEckRbU)abénmFümKMrUtag X ebIvaCaKMrUtagécdnüsamBaØGaRs½y.

cUrKNna mFüm nigva:rüg;én X edaypÞal;bnÞab;mkepÞógpÞat;CamYyRTwsþIbT.

dMeNaHRsaydMeNaHRsay

Tung Nget, MSc 6-12

dMeNaHRsay dMeNaHRsay ¬¬tt¦¦

Tung Nget, MSc 6-13

x- krNIKMrUtagécdnüsamBaØGaRs½yeyIg)an ³

eK)an taragbMENgEckKMrUtagénmFüm X nigFatusMxan;² dUcxageRkam ³

( ) ( ) ( ) ( )( ) ( )22i i i iX XE X X p X X 10 V X X E X p X X 19⎡ ⎤⎡ ⎤=μ = × = = =σ = − × = =⎣ ⎦ ⎢ ⎥⎣ ⎦∑ ∑eK)an nig


20

Tung Nget, MSc 6-14


RTwsþIbT 7 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØminGaRs½ymanTMhM n enaHsRmab; n FMlμm RKb;RKan; ( )n 30≥

eK)anEbgEckmFümKMrUtag X KWRbhak;RbEhl nwgbMENgEckn½rma:l;Edlman mFümnBVnþ μμ =X nigKmøatKMrU nXσσ = .

bMENgEckén X

X

XZ

−μ=

σ KWRbhak;RbEhl nwgbMENgEckn½rm:al;sþg;dar.

RTwsþIbT 8 ³ enAkñúgsaklsßitiEdlmanTMhMFM b¤ Gnnþ nigEdlmanmFüm μ nigKmøatKMrU σ yk n CaTMhMKMrUtagsamBaØ.

enaHsRmab; n FMlμmRKb;RKan; n 30≥ eK)anbMENgECkmFümKMrUtag X KWRbhak;RbEhl nwgbMENgEckn½rma:l;EdlmanmFümnBVnþ

μμ =X nigKmøatKMrU nXσσ = . bMENgEckén X

X

XZ

−μ=

σ KWRbhak;RbEhl nwgbMENgEckn½rm:al;sþg;dar.

RTwsþIbT 9 ³ ebIsaklsßitimanbMENgEckn½rma:l;EdlmanmFüm μ nigKmøatKMrU σ yk n CaTMhMKMrUtagsamBaØ enaHRKb; n 1≥

eK)an bMENgEckénmFümKMrUtag X KWmanbMENgEckn½rma:l;EdlmanmFüm μμ =X nigKmøatKMrU nXσσ = .

bMENgEckén X

X

XZ

−μ=

σ KWmanbMENgEckn½rma:l;sþg;dar.

( ) ( ) ( ) ( )( ) ( )22i i i iX SE X X p X X 10 V X X E X p X X 14.25⎡ ⎤⎡ ⎤=μ = × = = =σ = − × = =⎣ ⎦ ⎢ ⎥⎣ ⎦∑ ∑eK)an nig

Tung Nget, MSc 6-15


2-bMENgEckKMrUtagkm μénmFümKMrUtag ¬]TahrN_¦

Rkumhu‘nGKÁisnImYyp;litGMBUlePøIgEdlGayurbs;vaRbhak;RbEhl

nwgbMENgEckn½rma:l;EdlmanmFümes μ I 800 ema:g nigKmøatKMrU 40

ema:g. KMrUtagécdnümYymanTMhM 64 GMBUl.

1- cUrKNnaRbU)abedIm,I[GMBUlTaMg 64 enHmanGayukalCamFüm³

k- enAcenøaHBI 780 dl; 815 .

x- FMCag 785 .

K- ticCag 775 .

2- cUrKNnaPaKryénKMrUtagEdlmanGayukalCamFümenAcenøaHBI

785 ema:geTA 810 ema:g.

1- X manbMENgEckRbhak;RbEhl nwgr)ayn½rma:l;Edl ³

X x

40800 5n 64σ

μ = μ = σ = = =nig.

k- eK)an ( ) ( )21815780 zZzPXP <<=<< Edl ³

X1

X

X2

X

780 780 800z 45

815 815 800z 35

−μ −= = = −

σ

−μ −= = =

σ

( ) ( )( ) ( )( ) ( )

P 780 X 815 P 4 Z 3

P 4 Z 0 P 0 Z 3

P 0 Z 4 P 0 Z 3

< < = − < <

= − < < + < <

= < < + < <

0.49997 0.49870 0.99867= + =

dUcenH ( ) 9987.0815780 =<< ZP .

x- eK)an ( ) )(785 zZPXP >=> Edl 35

800785785−=

−=

−=

X

Xzσ

μ

( ) ( ) ( )

9987.04987.05000.0305000.03785

=+=<<+=−>=> ZPZPXP

dUcenH ( ) 9987.0785 =>XP .

K- eK)an ( ) ( )P X 775 P Z z< = < Edl X

X

775 775 800z 55

−μ −= = =

σ

( ) ( ) ( )P X 775 P Z 5 0.5000 P 0 Z 5

0.5000 0.4999 0.0001

= − = < <

= =

< < −

−

dUcenH ( ) 0001.0775 =<XP .

Tung Nget, MSc 6-16


2- eK)an ( ) ( )1 2P 785 X 810 P z Z z< < = < < Edl

X1

X

X2

X

785 785 800z5

810 810

3

8 200z5

−μ −⎧ = = =⎪ σ⎪⎨ −μ −

=

−

⎪ = =⎪ σ⎩

( ) ( ) ( ) ( )

9759.047724987.0203023810785

=+=<<+<<=<<−=<< ZPZPZPXP

dUcenH PaKryénKMrUtagEdlmanGayukalCamFümenAcenøaHBI 785 ema:geTA 810

ema:gKW 97/59°.

Tung Nget, MSc 6-17

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )AA A X A

2 2A APs Ps Ps

N n N nE X np, V X np 1 p , V X np 1 pN 1 N 1

p 1 pX X N nE Ps E p, V Ps V &n n N 1 n

⎧ − −= = − σ = = −⎪ − −⎪

⎨−−⎛ ⎞ ⎛ ⎞⎪ = = σ = = = σ = σ⎜ ⎟ ⎜ ⎟⎪ −⎝ ⎠ ⎝ ⎠⎩

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

AA A X A

2As Ps Ps

E X np, V X np 1 p , V X np 1 p

p 1 pXE P E p, V Ps , V Psn n

⎧ = = − σ = = −⎪⎨ −⎛ ⎞= = σ = = σ =⎪ ⎜ ⎟

⎝ ⎠⎩

3>bMENgEckKMrUtagkmμénsmamaRt ¬Sampling distribution of the proportion¦

eKmansaklsßitimYyEdlmanTMhM N . yk NA CacMnYnFatuénsaklsßitiEdlmanlkçN³ A eKehA ³

NNp A= faCasmamaRténsaklsßiti ¬Population proportion¦. ecjBIsaklsßitienHeK eRCIserIsKMrUtagécdnüsamBaØmYy

EdlmanTMhM n Edl ³ X1, X2,…Xn-1 nig Xn CatémøEdlTTYl)an. yk XA CacMnYnFatuenAkñúgKMrUtagEdlmanlkçN³ A .

eK)an ³ XA = X1+X2+…Xn nig nXP A

s = faCasmamaRtKMrUtag ¬sample proportion¦.

RTwsþIbT 10 ³

- ebIKMrUtagécdnüEdlmanTMhM n enHCaKMrUtagécdnüsamBaØminGaRs½yEdlykecjBIsakl sßitiEdlmanTMhM N b¤ TMhMGnnþenaH

XA CaGefreTVFa nigeKTaj)anrUbmnþ ³

- ebIKMrUtagécdnüEdlmanTMhM n enHCaKMrUtagécdnüsamBaØGaRs½yEdlykecjBIsaklsßiti EdlmanTMhM N enaH

XA CaGefrGuIEBrFrNImaRt nigeKTaj)anrUbmnþ³

Tung Nget, MSc 6-18

- ebIKMrUtagécdnüEdlmanTMhM n enHCaKMrUttagécdnüsamBaØGaRs½yEdlykecjBIsaklsßiti

EdlmanTMhMGnnþenaH XA CaGefrGuIEBrFrNImaRt nigeKTaj)anrUbmnþ ³

3>bMENgEckKMrUtagkmμénsmamaRt ¬t¦

RTwsþIbT 11 ³ enAkñúgsaklsßitiEdlmanTMhM N b¤ Gnnþ nigKMrUtagécdnüEdlmanTMhM n

enHCaKMrUtagécdnüsamBaØminGaRs½ykalNa n kan;EtFMenaHGefrécdnü Ps

s pPZσ−

= Edl

( ) ( )Ps

p 1 pV Ps

n−

σ = = manbMENgEckRbhak;RbEhlnwgbMENgEckn½rm:al;sþg;dar.

RTwsþIbT 12 ³ enAkñúgsaklsßitiEdlmanTMhM N b¤ Gnnþ nigKMrUtagécdnüEdlmanTMhM n

enHCaKMrUtagécdnüsamBaØGaRs½ykalNa n kan;EtFMenaHGefrécdnü Ps

s pPZσ−

= Edl ³

( ) ( )Ps

p 1 pN nV PsN 1 n

−−σ = =

− manbMENgEckRbhak;RbEhl nwgbMENgEckn½rm:al;sþg;dar.

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )AA A X A

2As Ps Ps

E X np, V X np 1 p , V X np 1 p

p 1 p p 1 pXE P E p, V Ps , V Psn n n

⎧ = = − σ = = −⎪⎪⎨ − −⎛ ⎞⎪ = = σ = = σ = =⎜ ⎟⎪ ⎝ ⎠⎩

Tung Nget, MSc 6-19

]TahrN_ ³ eKdwgfa 60 ° énGñke)aHeqñatnwge)aHeqñat[KNbkS A. cUrKNnaRbu)abEdl

naM[KMrUtagécdnüsamBaØEdlmanTMhM 160 EdlsmamaRténGñke)aHeqñat[KNbkS A mantic

Cag 50 ° .


eKman p=60%=0.60 CasmamaRténGñke)aHeqñat[KNbkS A rbs;saklsßiti nig

ps CasmamaRtGñke)aHeqñat[KNbkS A rbs;KMrUtagécdnü. eK)an³

( ) ( ) ( )

( ) ( )( )

sPs

Ps

s

Ps

s

0.5

p 1 p 0.60 1 0.60P pZ V Ps 0.049n 100

P p 0.60Z 2.040.049

p p 0.5 p Z 2.04

p Z 2.04

0

− −−= σ = = = =

σ

− −= = = −

σ

< = < −

= >

Edl

deU cHñ

Tung Nget, MSc 6-20


k>k> krNIminGaRs½y ¬eRCIsedaydak;eTAvij¦

( ) ( )

( )

( )

sPs

Ps

s

Ps

s

10.

p 1 pP pZ V Psn

0.50 1 0.500.1291

15

0.50P pZ 1.550.1291

10.5p p p Z 1.55 0.06

5

1

5

15

1

−−= σ = =

σ

−= =

−−= = =

σ

⎛ ⎞> = > =⎜ ⎟⎝ ⎠

Edl

deU cñH

]TahrN_ ³ kñúgcMeNamTMnijTaMg 100 Edl)ansþúkTukman 50 xUc. Pñak;garRtYtBinitü

EdlminsÁal;tYelxenH nwgeRCIserIsykTMnij 15 CaKMrUtagécdnüsamBaØ.

cUrKNnaRbU)abEdlnaM[manTMnijxUceRcInCag 10 TaMgkrNIminGaRs½y nigkrNIGaRs½y.

3>bMENgEckKMrUtagkm μénsmamaRt ¬]TahN_¦

CMhanTI1³ rksmamaRténTMnijxUckñúgsaklsßiti nigKMlatKMrUénbMENgEckeTVFa nig

rk z EdlRtUvK μanwg ps= 10.5/15 ¬X+ 0.0.5 KWCaktþaEktRmUvPaBCab;BIeTVFamkn½rma:l;¦

CMhanTI2³ kMNt;épÞcab;BI ps= 10.5/15 eLIg.

eKman smamaRténTMnijxUckñúgsaklsßiti p=50/100=0.50

cMNaMcMNaM³³ kareFVIkMENPaBCab;cMeBaHEtKMrUécdnümanTMhMtUc.

Tung Nget, MSc 6-21


k>k> krNIGaRs½y ¬eRCIsedaymindak;eTAvij¦

( ) ( )

( )

( )

sP s

Ps

s

Ps

s

p 1 pP p N nZ V P sN 1 n

0.50 1 0.50100 15 0.1196100 1 15

0.50P pZ 1.

10.51 67

0.119610.5p p p Z 1.6715

5

−− −= σ = =

σ −

−−= =

−

−−= = =

σ

⎛ ⎞> = >⎜ ⎟⎝ ⎠

Edl

d Uec ñH

]TahrN_ ³ kñúgcMeNamTMnijTaMg 100 Edl)ansþúkTukman 50 xUc. Pñak;garRtYtBinitü

EdlminsÁal;tYelxenH nwgeRCIserIsykTMnij 15 CaKMrUtagécdnüsamBaØ.

cUrKNnaRbU)abEdlnaM[manTMnijxUceRcInCag 10 TaMgkrNIminGaRs½y nigkrNIGaRs½y.

3>bMENgEckKMrUtagkm μénsmamaRt ¬]TahN_¦

eKman smamaRténTMnijxUckñúgsaklsßiti p=50/100=0.50

Tung Nget, MSc 6-22

4> témø)a:n;s μanCacMNuc nigcenøaHTukcitþ ¬Point estimates and Confidence intervals¦

Ca]TahrN_ mFümKMrUtag X Catémø)a:n;s μanén mFümsaklsßiti μ cMENk

smamaRtKMrUtag sp Catémø)a:n;s μanénsmamaRtsaklsßiti p .

yk θ Ca)a:ra:Em:RtminsÁal;énsaklsßitimYy. ecjBIsaklsßitienH eKeRCIserIsKMrUtagécdnümYyEdl

manTMhM n nigmanGefrécdnü X1 ,X2,…Xn-1 nig Xn bnÞab;mkeKKNna témøsßiti θ minlem¥ógmYyén θ .

ttéémmøø)a:n;s)a:n;s μμan an CacMNucCatémøEdlKNna)an BIB½t’manKMrUtag nig

RtUv)aneKeRbIedIm,IeFVICa témø)a:n;sμan)a:ra:Em:Rténsaklsßiti.

cencen øø aHTukcitþ aHTukcitþ CacenøaHEdlKNna)anBIB½t’manKMrUtagedIm,I [)a:ra:Em:Rténsaklsßiti sßitenAkñúgcenøaHenH Rtg;RbU)abCak;lak;mYy. RbU)abCak;lak;EdleKR)ab;enH ehAfakRmitTukcitþ ¬Level of confidence¦ . cenøaHenHehAfatémø)a:n;sμanCacenøaH.

eK)aneK)an³³ ( )

k

k

1p k k 1 ,

k k:Confidence level

k:Sgnificance

⎧θ−⎪⎪θ+⎪−α⎪θ− ≤ θ ≤ θ+ = −α ⎨θ− ≤ θ ≤ θ+⎪⎪⎪⎪α⎩

t

CaeKaleRkam

CaeKalelI

CakRmitTukcti

CakMhsu KrM U

μX

k

Tung Nget, MSc 6-23

4> karbkRsaytémø)a:n;s μan ¬Interval Estimates- Interpretation¦

cMeBaHcencMeBaHcenøø aHTukcitþ aHTukcitþ 95%95% manRbEhlCa manRbEhlCa 95%95% ééncenncenøø aHTaMgLayEdlRtUv)ansg; nwgpÞaHTaMgLayEdlRtUv)ansg; nwgpÞ úúk)a:ra:Em:tEdl k)a:ra:Em:tEdl

RtUv)a:n;sRtUv)a:n;s μμan. ehIy an. ehIy 95%95% éénmFnmFüümKMrUtagsRmab;TMhMKMrUtagCak;lak;mYy nwgsmKMrUtagsRmab;TMhMKMrUtagCak;lak;mYy nwgsßß itenAkitenAk ñúñúgKmgKmøø atKMrUatKMrUéén n

saklssaklsßß itiEdlRtUveFVIetsþ.itiEdlRtUveFVIetsþ.

sMNakén X

mFümsaklsßiti

KMrUtag ! TMhM 256 pÞúkmFümsaklsßiti

KMrUtag @ TMhM 256 pÞúkmFümsaklsßiti

KMrUtag # TMhM 256 pÞúkmFümsaklsßiti

KMrUtag $ TMhM 256 pÞúkmFümsaklsßiti

KMrUtag % TMhM 256 minpÞúkmFümsaklsßiti

KMrUtag 6 TMhM 256 pÞúkmFümsaklsßiti

1X

2X

3X4X

5X6X

Tung Nget, MSc 6-24

rebobKNnatémø Z edaysÁl;cenøaHTukcitþ

¬ How to Obtain z value for a Given Confidence Level ¦

cenøaHTukcitþ 95% KWCaEpñkkNþal 95% éntémøGegát.

dUecñH enAsl; 5% RtUvEckCaBIresμIKñarvagcugTaMgsgxag.

tamtarag Appendix B.1.

cenøaHTukcitþ

90% 0.10 0.0595% 0.05 0.02599% 0.01 0.005

α2α

2

zα( )1 100%−α

2 2

p 0 Z z 0.4750 z 1.96α α

⎛ ⎞⇒ < < = ⇒ =⎜ ⎟

⎝ ⎠tamtarag

2 2

p z Z z 1α α

⎛ ⎞− < < + = −α⎜ ⎟⎝ ⎠

2

z α−

2α ( )1−α

2

z α

0

2α

cenøaHTukcitþ

90% 0.10 0.05 1.6595% 0.05 0.025 1.9699% 0.01 0.005 2.575

α2α

2

zα( )1 100%−α

Tung Nget, MSc 6-252 2

p z Z z 1α α

⎛ ⎞− < < + = −α⎜ ⎟⎝ ⎠

cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIsÁal;

cenøaHTukcitþsRmab;mFümsaklsßiti edaysÁal; KW³

2 2

N n N nX z . X z .N 1 N 1n nα α

σ − σ −− ⋅ ≤ μ ≤ + ⋅

− −

2

z α−

2α

2α

1−α

2

z α0

X k−

2α

2α

1−α

μ X k+

σ

σ2

X z .nασ

±

x σ Nn z

mFümKMrUtag

KmøatKMrUsaklsßiti

témø Z cMeBaHcenøaHTukcitþCak;lak;NamYy

cMnYntémøGegátsrubkñúgKMrUtag (>30)TMhMsaklsßitiminsÁal;

2 2

X z X zn nα ασ σ

− ⋅ ≤ μ ≤ + ⋅

cenøaHTukcitþsRmab;mFümsaklsßiti

edaysÁal; KW³σ2

N nX z .N 1nα

σ −± ⋅

−

x σ Nn z

mFümKMrUtag


témø Z cMeBaHcenøaHTukcitþCak;lak;NamYy

cMnYntémøGegátsrubkñúgKMrUtag (>30)TMhMsaklsßitisÁal;

( )p X k X k 1− <μ< + = −α

N n 1N 1−

→−

ebI n/N < 0.05RtUveRbI (*) (*)

eRBaH

((*) *)

Tung Nget, MSc 6-26

]TahrN_]TahrN_³³ eKeRCIserIsKMrUécdnücMnYn64)avBIkñúgsaklsßiti)avsIum:g;EdlmFümsaklsßiti minsÁal;

ehIymanKmøatKMrU KILÚRkam bnÞab;BIføwgrYceKdwgfaTMgn;mFüm edayykcenøaHTukcitþes μI

95% cUrkMnt;cenøaHeCOCak;TMgn;sIum:g;énsaklsßiti ebIKMrUtagécdnüCaKMrUécdnüsamBaØminGaRs½y.

μ

4σ = X 48kg=


cenøaHTukcitþsRmab;mFümsaklsßitiKW³

2 2

0.0252

4X z . 48 z .n 64

1 0.95 z z

α α

α

σ± = ±

− α = ⇒ = =

cenøaHTukcitþsRmab;mFmFüümsaklsmsaklsßß itiitikñúgkrNIsÁal; ¬]TahrN_¦σ

2 2

0.0252

2

4X z . 48 z .n 64

1 0.95 z z 1.96

4X z 48 1.96 48 0.98n 64

47.02 48.98

α α

α

α

σ± = ±

− α = ⇒ = =

σ± ⋅ = ± × = ±

⇒ ≤ μ ≤

Tung Nget, MSc 6-27

]TahrN_]TahrN_³³ eKeRCIserIsKMrUécdnücMnYn64)avBIkñúgsaklsßiti)avsIum:g;EdlmFümsaklsßiti minsÁal;

ehIymanKmøatKMrU KILÚRkam bnÞab;BIføwgrYceKdwgfaTMgn;mFüm edayykcenøaHTukcitþes μI

99% cUrkMnt;cenøaHeCOCak;TMgn;sIum:g;énsaklsßiti ebIKMrUtagécdnüCaKMrUécdnüeRCIseday

mindak;eTAvijBIsaklsßitiTMhM N=1000)av.

μ

4σ = X 48kg=


cenøaHTukcitþsRmab;mFümsaklsßitiKW³

2

0.0052

2

N nX z .N 1n

1 0.99 z z 2.575

N n 4 1000 642.575 1.241000 16

X z . 48 48N 1n

46.76 49.244

α

α

α

σ −± ⋅

−

−α = ⇒ =

−×

=

σ −± ⋅ = ± = ±

−

⇒ ≤μ ≤

−

cenøaHTukcitþsRmab;mFmFüümsaklsmsaklsßß itiitikñúgkrNIsÁal; ¬]TahrN_¦σ

2

0.0052

N nX z .N 1n

1 0.99 z z

α

α

σ −± ⋅

−

−α = ⇒ = =

Tung Nget, MSc 6-28

krNIminsminsÁÁal;al;KmøatKMrUsaklsßiti => bMENgEck tt

enAkñúgsßanPaBeFVIKMrUtag CaFm μta eKminsÁal;KmøatKMrUsaklsßiti (σ).

σ

lklkççNN³é³énbMENgEck nbMENgEck tt³³1>¦ vaCabMENgEckCab; dUcbMENgEck Z Edr

2>¦ vamanragCaCYYg nigsIuemRTI dUcbMENgEck Z Edr

3>¦ minEmnCabMENgEck t EtmYyenaHeT EtvaCaRKYsar

énbMENgEck t. bMENgEck t TaMgGs;man mFüm = 0

b:uEnþmanKmøatKMrUERbRbYlGaRs½ynwgTMhMénKMrUtag/ n

4>¦ bMENgEck t manlkçN³latnigTabenARtg;cMNuckNþalCag

bMENgEcknr½ma:l; EteTaHCaya:gNa bMENgEck t xitCitbMENg

Ecknr½ma:l;.

etIsÁal;KmøatKMrUsaklsßitirWeT?etIsÁal;KmøatKMrUsaklsßitirWeT?

sn μt;CamunfasaklsßitieKarBtamc,ab;nr½ma:l;

sn μt;CamunfasaklsßitieKarBtamc,ab;nr½ma:l;

cUreRbIbMENgEck Z cUreRbIbMENgEck Z cUreRbIbMENgEck tcUreRbIbMENgEck t

YesΝο n > 30r Wn <30ngi

2

C.I : X z .nασ

±

2

s N nC.I : X t .N 1nα−

±−

2

sC.I : X t .nα±

2

N nC.I : X z .N 1nα

σ −±

−

Tung Nget, MSc 6-29N n 1N 1−

→−

2

t α−

2α

2α

1−α

2

t α0

cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIminsminsÁÁal;al;


eRCIsdak;eTAvijeRCIsdak;eTAvijKW³

2 2

s N n s N nX t . X t .N 1 N 1n nα α− −

− ⋅ ≤ μ ≤ + ⋅− −

σ

2

sX t .nα±

2 2

s sX t X tn nα α− ⋅ ≤ μ ≤ + ⋅


eRCIsmindak;eTAvijeRCIsmindak;eTAvijKW³2

s N nX t .N 1nα−

± ⋅−

2

x s N

n t α

σ

mFümKMrUtag

KmøatKMrUénKMrUtag

témø cMeBaHcenøaHTukcitþCak;lak;NamYy

cMnYntémøGegátsrubkñúgKMrUtag (<30)

TMhMsaklsßitiminsÁal;

2

tα

KmøatKMrUénsaklsßitiminsÁal;

2

x s N

n t α

σ

mFümKMrUtag

KmøatKMrUénKMrUtag


cMnYntémøGegátsrubkñúgKMrUtag (<30)

TMhMsaklsßitisÁal;

2

tα

KmøatKMrUénsaklsßitiminsÁal;

ebI n/N < 0.05RtUveRbI (**) (**)

eRBaH

finite population correction factor

(**)(**)

Tung Nget, MSc 6-30

]TahrN_]TahrN_³³ eragcRksMbkkg;mYycg;eFVIkarGegátBIGayukal

RkLasMbkkg;rbs;xøÜn. KMrUtagTMhM !0sMbkkg;RtUv)aneRbIkñúgkar

ebIkbrcMgay %0/000ma:y )anbgðan[dwgfamFümKMrUtagesμI

0>#@ Gij énRkLakg;enAsl; edaymanKmøatKMrUesμI 0>0( Gij.

1>¦ cUrsg;cenøaHTukcitþ (%% sRmab;témøCamFümsaklsßiti.

2>¦ etIvasmehtuplEdrrWeTcMeBaHeragcRkkñúgkarsnñidæanfa

bnÞab;BI %0/000 ma:y brimaNmFümsaklsßitiénRkLakg;Edl

enAsl; KwesμI 0>30 Gij?

μcenøaHeCOCak;sRmab; ¬]TahrN_edayeRbIbMENgEck tt¦

0.5, n 1 , 10 12 2

C.I. ts sX t X tn nα

− −± × = ± ×

σ1 >¦ KNna edayeRbIbMENgEck ¬eRBaH minsÁal ; ¦

2>¦ snñidæan³ eragcRkGacR)akdd¾smehtuplfaCeRmARkLa EdlenAsl;CamFümKWenAcenøaHBI 0>@%^ eTA 0>#*$ Gij.

[ ]

0.5, n 1 , 10

0.0 9

12 2

25,t

2

C.I. ts sX t X tn n

0.090.3210

0.090.3210

0.32 0.064 0.256,

.

0.38

2

4

62

α− −

± × = ± ×

= ± ×

= ± ×

= ± =

σ1>¦ KNna edayeRbbI MENgEck ¬eRBaH mni saÁ l ; ¦

Tung Nget, MSc 6-31

mFümsaklsßitiTMngCaFMCag $432 b:unEnþ tUcCag $468.

mFümsaklsßitiGaces μ I $445 b:uEnþ mines μ I $425eT eRBaH $445

sßitenAkñúgcenøaHTukcitþ cMENk $425 minenAkñúgcenøaHenHeT.

]TahrN_]TahrN_³³ manRKYsarcMnYn @%0 enAkñúg Scandia,

Pennsylvania. KMrUtagécdnüTMhM 40 énRKYsar

TaMgenH)an[dwgfa karbricakcUlkñúgRBHviha

RbcaMqñaMKWes μ I $450 nigKmøatKMrUénKMrUtagenHKW $75.

etImFümsaklsßitiGacesμ I $445 rW $425 EdrrWeT?

etImFümsaklsßities μ Inwgb:un μan?

rktémø)a:n;sμan 90% sRmab;mFümsaklsßiti.

tambRmab;³

μcenøaHeCOCak;sRmab; edaymanktþaEktRmUvsaklsßitikMNt; ¬]TahrN_¦

[ ]

0.052

s $75 250 40X $450 z250 1n 40

$75 250 40 $450 1.65250 140

$450 $19.57 0.8434 $450 $18 $432, $4

z N nN 1

68

α−

± = ±−

−= ±

−

= ±

= ± =

−−

N = 250n = 40s = $75

eday dUecñHRtUveRbI

ktþaEktRmUvsaklsþitikMNt;. eKminsÁal;

KmøatKMrUsaklsßiti KUeRbIbMENgEck bMENgEck t t Et n>30

=> eRbIbMENgEck Z .

n 40 0.16N 250

= =

Tung Nget, MSc 6-32

cenøaHTukcitþsRmab;smamaRtsaklsßitikñúgkrNIssÁÁal;al;

cenøaHTukcitþsRmab;smamaRtsaklssmamaRtsaklsßß ititi

eRCIsdak;eTAvijeRCIsdak;eTAvijKW³

σ

( ) ( )2 2

Ps 1 Ps Ps 1 PsPs z p Ps z

n nα α

− −− ≤ ≤ +

cenøaHTukcitþsRmab;smamaRtsaklssmamaRtsaklsßß iti iti

eRCIsmindak;eTAvijeRCIsmindak;eTAvijKW³

s

2

pN

n Zα

σ

smamaRtKMrUtag


cMnYntémøGegátsrubkñúgKMrUtag (>30)

TMhMsaklsßitiminsÁal;

2

Zα

KmøatKMrUénsaklsßitisÁal;

2

z α−

2α

2α

1−α

2

z α0

( )2

Ps 1 PsPs z

nα

−±

( )2

Ps 1 Ps N nPs zn N 1α

− −±

−

( ) ( )2 2

Ps 1 Ps Ps 1 PsN n N nPs z p Ps zn N 1 n N 1α α

− −− −− ≤ ≤ +

− −

s

2

pN

n Zα

σ

smamaRtKMrUtag


cMnYntémøGegátsrubkñúgKMrUtag (>30)

TMhMsaklsßitisÁal;

2

Zα

KmøatKMrUénsaklsßitisÁal;

2 2

p z Z z 1α α

⎛ ⎞− < < + = −α⎜ ⎟⎝ ⎠

finite population correction factor

N n 1N 1−

→−

ebI n/N < 0.05RtUveRbI (***) (***)

eRBaH

((***) ***)

Tung Nget, MSc 6-33

cenøaHTukcitþsRmab;smamaRtsaklsßiti ¬]TahrN_¦

[ ]

s

s ss / 2

:x 1,600p 0.80n 2000

95% C.I.

p (1 p )C.I. p zn0.80(1 0.80) 0.80 1.96 0.80 0.018

2,000 0.782, 0.818

α

= = =

−= ±

−= ± = ±

=

dMbgU / KNnasmamaRténKMrUtag

KNna

0

]TahrN_]TahrN_³³ shKmtMNag[ BBA kMBugBicarNa elIsMeNIrbBa¢ÚlKñaCamYy Teamsters Union. eyagtamc,ab;shKm BBA ya:gehacNas; 3/4

énsmaCikPaBshKm RtUvEtyl;RBmcMeBaH kardak; bBa©ÚlKña. KMrUtagécdnüénsmaCik BBA bc©úb,nñcMnYn @/000nak; )an[dwgfa !/^00nak; manKeRmage)aH eqñatKaMRTsMeNIrbBa©ÚlKñaenH. cUrKNnasmamaRtsaklsßiti.

cUrsg;cenøaHTukcitþ 95% sRmab;smamaRtsaklsßiti. edayEp¥kelIkarseRmccitþrbs;Gñk elIB½t¾mankñúg KMrUtag etIGñkGacsnñidæanfasmamaRtcaM)ac;énsmaCik BBA eBjcitþcMeBaHkarbBa©ÚlKñaEdrrWeT? ehtuGVI?


snñidæan³ sMeNIrdak;bBa©ÚlKñanwgTMngCaGnum½t)an

eRBaHenøaH)a:n;s μanpÞúktémøFMCag 75% énsmaCikPaB.

Tung Nget, MSc 6-34

cenøaHTukcitþsRmab;smamaRtsaklsßiti ¬]TahrN_¦

s

s ss / 2

:xp 0.10n

95% C.I.

p (1 p )C.I. p zn0.10(1 0.10) 0.10 1.96 0.10 0.083

50

α

= =

−= ±

−= ± = ±

k > dMbUg/ KNnasmamaRténKrM Utag

KNna

0

]TahrN_]TahrN_³³shRKasplitkg;LanmYyplitkg;LanCaeRcIn. edIm,IBinitüemIlPaBsViténkg;LangTaMgenaH eKeRCIs edayécdnünUvkg;LancMnYn n=50 CaKMrUtagécdnü. eKGegáteXIjfamankg;Lan 10% mineqøIytbnwg sMNUmBr. cUrkMNt;cenøaHTukcitþ sRmab;smamaRt pénkg;LanTaMgGs;EdlplitmintamsMNUmBr eday ykkMritTukcitþ 95% ebI³

k>k> KMrUtagCaKMrUtagminGaRs½y.

x>x> KMrUécdnüCaKMrUécdnüeRCIsmindak;eTAvij nigLanEdlplitTaMgGs;mancMnYn 400kg;.


( )

s

s ss /2

xp 0.10n

95% C.I.

p (1 p ) N nC.I. p zn N 10.10(1 0.10) 400 50 0.10 1.96

50 400 10.10 1.96 0.04 0.10 0.0784 [0.0218, 0.1784]

α

= =

− −= ±

−

− −= ±

−= ± × = ± =

x> dMbgU / KNnasmamaRténKrM Utag

KNna

Tung Nget, MSc 6-35

22

/znE

α ⋅σ⎛ ⎞= ⎜ ⎟⎝ ⎠

kareRCIserIsTMhMKMrUtagd¾smRsb

0

manktþa 3ya:gEdlkMNt;TMhMKMrUtag EdlK μanktþa NamYymanTMnak;TMngedaypÞal; cMeBaHTMhM saklsßitieT.1.) kMritTukcitþEdlcg;)an2.) kMritel¥ógEdlGñkRsavRCavnwgTTYyk)an3.) karERbRbYlkñúgsaklsßitiEdlkMBugRtUvsikSa

dMeNaHRsaydMeNaHRsay2

/ 2

22

znE

(1 .96)($1, 000) (19 .6)$100

384 .16 385

α ⋅ σ⎛ ⎞= ⎜ ⎟⎝ ⎠

⎛ ⎞= =⎜ ⎟⎝ ⎠

= =

Edl ³

/2

nz

E

α

σ

TMhMKMrUtag

Catémønr½ma:l;KMrUEdlRtUvKñanwgkMrit TukcitþEdlcg;)an


kMhusEdlGacGnuBaØat[manFMbMput

]TahrN_]TahrN_³³

nisSitenAkñúgrdæ)alsaFarNcg;kMNt;brimaN mFümEdlsmaCikénRkumRbwkSaRkugkñúg TIRkugFM² rkcMNUl)ankñúgmYyExBIkareFVICa smaCik. kMhuskñúg kar)a:n;s μanmFümKWRtUv tUcCag $100 edaymancenøaHTukcitþ 95%. nisSitenaH)anrkeXIjfar)aykarN_eday naykdæankargarEdl)an)a:n;sμanBIKmøatKMrUKW RtUvesμ I $1,000. etIeKRtUvkareRCIserIsTMhM KMrUtagEdlRtUvkarb:un μan?

Tung Nget, MSc 6-36

21.96n (0.30)(0.70) 8970.03

⎛ ⎞= =⎜ ⎟⎝ ⎠

kareRCIserIsTMhMKMrUtagedIm,I)a:n;sμansmamaRtsaklsßiiti

0


Edl ³

/2

nz

E

α

σ

TMhMKMrUtag

Catémønr½ma:l;KMrUEdlRtUvKñanwgkMrit TukcitþEdlcg;)an


kMhusEdlGacGnuBaØat[manFMbMput

]TahrN_]TahrN_³³

/ 22Zn p(1 p)

Eα⎛ ⎞= − ⎜ ⎟

⎝ ⎠

21.65n ( 0̀.5)(1 0.5) 68.06250.10

n 69

⎛ ⎞= − =⎜ ⎟⎝ ⎠

= TRI kgu

nPaB émanGMBIRbU)ab¾t½anBμebIK³³cMNaMcMNaMeCaKC½y eyIgyk p = 0.5.

køib American Kennel Club cg;)a:n;s μansmamaRt

ének μgEdlmanEqáCastVciBa©wm.RbsinebIkøwbenHcg; )ankar)a:n;s μanEdlRtUvCamYy 3% énsmamaRt saklsßiti etIBYkeKRtUvTak;TgsmÖasn_ek μg²cMnYn b:un μannak;? sn μt;cenøaHTukcitþes μ I 95% ehIykøwbenH )an)a:n;s μanfa 30%ének μg²manEqáCastVciBa©wm.

karsikSamYyRtUvkar)a:n;sμanBIsmamaRténTIRkug EdlmanGñkcak;sMramÉkCn. GñkGegátcg;)an kRmitkMhusRtUvCamYy 0.10 énsmamaRtsakl sßiti nigkRmitTukcitþKWes μ I 90 PaKry ehIyK μan kar)a:n;sμanNamYysþIGMBIsmamaRtsaklsßitieT. etIeKRtUvakarTMhMKMrUtagb:un μan?

]TahrN_]TahrN_³³

Tung Nget, MSc 6-37

cb;edaybribUN_

GrKuNcMeBaHkarykcitþTukdak;¡rrr<sss

estimation and confidence intervals

Technology

nsansmamartsaklsiti

random sample ekerbiedim

nitra mankmkrsrub cmnyn

aybitegvi edim

kmrutagcdnsamba garsy

npab50011 edim

epkktn nn

msc46 erciseristmhmkmrutagedim