1. CMBUkTI 6
bMENgEckénKMrUtagkmμécdnü
sßitiBaNiC¢kmμ
eroberog nigbeRgonedaysa®sþacarü
Tug Eg:t
Tel: 017 865 064
E-mail: tungnget@yahoo.com
Website: www.nget99.blogspot.com
Tung Nget, MSc 6-1

2. bMENgEckénKMrUtagkmμécdnü
• 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 6-2

3. bMENgEckénKMrUtagkmμécdnü
• vtßúbMNg³ enAeBlEdlGñkbBa©b;enAkñúgCMBUkenH GñknwgGac³
8. KNnatémø Z edaysÁl;cenøaHTukcitþ
9. eRCIserIsTMhMKMrUtagd¾smRsb
10. eRCIserIsTMhMKMrUtagedIm,I)a:n;sμansmamaRtsaklsßiti
Tung Nget, MSc 6-3

4. bMENgEckénKMrUtagkmμécdnü
1> viFIeRCIserIsKMrUtagRbU)ab
2> bMENgEckKMrUtagkmμénmFümKMrUtag
3> bMENgEckKMrUtagkmμénsmamaRt
4> témø)a:n;sμanCacMNuc 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 6-4
Tung Nget, MSc
4>6> eRCIserIsTMhMKMrUtagedIm,I)a:n;sμansmamaRtsaklsßiti

5. 1-kareRCIserIsKMrUtagRbU)ab (Selecting the Probability Sample)
• ehtuGVIRtUveFVIKMrUtagkmμécdnü?
1> karsikSaelIsaklsßitiTaMgmUyKWRtUveRbIeBlyU
RtU
2> éføénkarsikSaelIRKb;FatuTaMgGs;rbs;saklsßitiGaceRcInhYsehtueBk
3> karminGacRtUtBinitüCak;EsþgelIRKb;FatuTaMgGs;kñúgsaklsßiti
4> kareFVIetsþxøHGaceFVI[vinasdl;lkçN³FmμCatirbs;saklsßiti
§
5> lTplKMrUtagKWRKb;RKan;¬GacykCakar)an¦
viFIsa®sþKMrUtagmanlkçN³RbU)abEdleKeRbICaerOy²man4KW³ - dMeNIrkareRCIserIsKMrUtagKWepþateTAelI
• KMrUtagécdnüsamBaØ (Simple Random Sample) karRbmUlRkumtMNagtUcénsaklsßiti.
• KMrUtagécdnüCaRbBn½§ (Systematic Random Sample) - KMrUtagEdl)annwgpþl;nUvB½t’manEdlGac
• KMrUtagécdnüBIRKb;Rkum (Stratified Random Sample) [eKeRbIedIm,IeFVIkar):an;sμanlkçN³énsakl
• KMrUtagécdnüBIRkumécdnümYycMnYn (Cluster Random Sample) sßitiTaMgmUl .
Tung Nget, MSc 6-5

6. KMrUtagécdnüsamBaØ nig KMrUtagécdnüCaRbBn½§
• KMrUtagécdnüsamBaØCaKMrUtagécdnüEdlKMrUtag KMrUtagécdnüCaRbBn§ CaKMrUtagécdnüEdlmanTMhM n
nImYy²man»kasesμIKña[eKeRCIserIs edaydMbUgerobFatuénsaklsßitiEdlman NFatu
ecjBIsaklsßiti. tamlMdab;NamYy.
• KMrUtagécdnüsamBaØEckecjCaBIrKW³ - bnÞab;mkeKEcksaklsßitiCa nRkumEdlRkumnImYy²
¬1¦ KMrUtagécdnüsamBaØminGaRs½y nig
man k Fatu (k = EpñkKt;én N/n ).
¬2¦ KMrUtagécdnüsamBaØ GaRs½y. - cMnuccab;epþImedayécdnüRtUv)aneRCIserIs bnÞab;mk
]TahrN_³ ]sSah_kmμ Nitra mankmμkrsrub cMnYn 845nak;.
Fatural;TI k RtUv)aneRCIserIsBIsaklsßiti.
KMrUtagénkmμkrcMnYn52nak; RtUveKeRCIserIsecjBIsakl ]TahrN_³ ]sSah_kmμ Nitra mankmμkrsrub cMnYn 845nak;.
sßitienaH. cUrGñkGFib,ayBITegVIenHedIm,I)anKMrUtagmYy KMrUtagénkmμkrcMnYn52nak; RtUveKeRCIserIsecjBIsakl
edayeRbIviFIsa®sþKMrUtagécdnüsamBaØ. sßitienaH. cUrGñkGFib,ayBITegVIenHedIm,I)anKMrUtagmYy
dMeNIrkar³ eKsresreQμaHrbs;kmμkrnImYy² dak;elIRkdas
edayeRbIviFIsa®sþKMrUtagécdnüCaRbBn. §
ehIydak;kñúgRbGb;mYy. bnÞab;mkRkLúk[esμIsac; dMeNIrkar³ dMbUgKNna k = EpñkKt;én N/n .
dMbUgeRCIsykRkdasmYysnøwkBIkñúgRbGb; edayminemIl. cMeBaH]sSah_kmμ Nitra eyIgKYeRCIserIsbBa¢Ikmμkrral;TI16
rUceKbnþdMeNIrkarenHrhUtKMrUtagénkmμkrcMnYn52nak; (845/52). KMrUtagécdnüsamBaØRtUveRbIkñúgkareRCIserIs
RtUv)aneRCIserIs. ykeQμaHdMbUg ¬BIkñúgcMenamelxerogTI1eTATI16¦ bnÞab;mk
Tung Nget, MSc
cUreRCIsykeQμaHrral;TI16 BIbBa¢IbnþbnÞab; rhUtKMr6-6Utagén
kmμkrcMnYn52nak; RtUv)aneRCIserIs.

7. KMrUtagécdnüBIRKb;Rkum (Stratified Random Sampling)
KMrUtagécdnüBIRKb;Rkum³ dMbUgeKEcksaklsßitiEdlmanTMhM N Ca k Rkumrg ¬dac;KñaBIr²¦ ehIyeKeRCIserIs
KMrUtagBIRKb;RkumnImYy². viFIenHmanRbeyaCn_ enAeBlsaklsßitiGacRtUv)aneKEckCaRkum²c,as;las;
edayEp¥kelIlkçN³rYmNamYy.
]TahrN_³ ]bmafaeyIgcg;sikSaBIkarcMNayelIkar PaBcMeNj
pSBVpSayBaNiC¢kmμ cMeBaHRkumh‘unFM²cMnYn352
kñúgshrdæGaemrik edIm,IkMNt;faetIRkumh‘unEdl Rkum ¬cMNUlRTBü¦ cMnYnRkumh‘un eRbkg;eFob cMnYnEdlRtUveRCIsCaKMrUtag
mancMNUlRTBüx<s; )ancMNayelIkarpSayBaNi 1 cab;BI 30 % eLIg 8 0>02 1*
C¢kmμkñúkarlk;nImYy²eRcInCagRkumh‘unEdlmancM 2 20 %-30 % 35 0>10 5*
NUlTab rI»nPaBEdrrWeT. 3 10 %-20 % 189 0>54 27
4 0 %-10 % 115 0>33 16
cUreRCIserIsKMrUtagRkumh‘unTMhM50tamviFIsaRsþ SRS. 5 »nPaB 5 0>01 1
edIm,I[R)akdfaKMrUtagKWCatMNagd¾RtwmRtUvrbs;Rkum srub 352 1>00 50
h‘unTaMg352/ Rkumh‘unTaMgGs;RtUveKEckCaRkum
tamPaKryéncMNUlRTBü ehIyKMrUtagEdl
smamaRtnwgTMhMeFobénRkumRtUveKeRCIserIs
edayécdnü.
Tung Nget, MSc 6-7

8. KMrUtagécdnüBI;RkumécdnümYycMnYn (Cluster Sampling)
KMrUtagécdnüBIRkummYycMnYn³ dMbUgeKEcksaklsßitiEdlmanTMhM N Ca k RkumrgtamFmμCatiEdlekIteLIg
kñúgEdntMbn; rWtamlkçN³déTeTot. bnÞab;mk RkumTaMgGs;RtUeKeRCIserIsedayécdnü ehIyKMrUtagRtUv
RbmUledayécdnüedaykareRCIserIsecjBIRkumnImYy².
]TahrN_³ ]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 6-8

9. 2-bMENgEckKMrUtagkmμénmFümKMrUtag
(Sampling distribution for the sample means)
bMENgEckKMrUtagkmμénmFümKMrUtagCabMENgEckRbU)ab‘ÍlIetEdlmanral;mFümKMrUtagTaMgGs;rbs;TMhM
ag
KMrUtagEdleK[EdlRtUv)aneRCIsecjBIsaklsßiti.
]TahrN_³ Rkumh‘un]sSahkmμmYymanbuKÁlikEpñkplitTaMg 1> mFümKsaklsßiti KwesμI $7.71 EdlrktamrUbmnþ³
Gs;7nak; ¬cat;TukfaCasaklsßiti¦. cMNUlRbcaMem:agrbs;
buKÁliknImYy² RtUveK[kñúgtaragxageRkam. 2> edIm,IQandl;bMENgKMrUtagénmFüm/ eyIgRtUveRCIserIsKMrUtag TMhM2Edl
1> cUrKNnamFümsaklsßiti. GacmanTaMgGs; edaymindak;vijecjBIsaklsßiti bnÞab;mkcUrKNna
2> cUrrkbMENgEckRbU)abénmFümKMrUtag cMeBaHKMrUtagTMhM2. mFüménKMrUtagnImYy². manKMrUtagEdlGacmanTaMGs;21.
N! 7!
C = n
= = 21
3> cUrKNnamFüménbMENgEck. n!( N − n ) ! 2!( 7 − 2 )!
N
cMNYl cMNYl
4> etIeKGacGegáteXIjya:gdUecþcsþIGMBIsaklsßiti nig KMrUtag buKÁlik RbcaMem:ag KMrUtag buKÁlik RbcaMem:ag
bMENgEckKMrUtagkmμ.
buKÁlik cMNYlRbcaMem:ag buKÁlik cMNYlRbcaMem:ag
3> μX =
plbkénmFümKMrUtagTaMgGs; ; = $7.00 + $7.50 + ... + $8.50
U
cMnYnKMrUtagsrub 21
Tung Nget, MSc 6-9
$162
= = $7.71
21

10. 2-bMENgEckKMrUtagkmμénmFümKMrUtag ¬RTwsþIbT¦
RTwsþIbT 1 ³ X1,X2,..,Xn CaGefrécdnüenaH X , S 2
& S k¾CaGefrécdnüEdr.
RTWsþIbT 2 ³ ebIsaklsßitimanmFüm μ nigva:rüg; σ enaHtémøsgÇwmén Xi cMeBaHRKb; i = 1,2,…,n KW³
2
E ( X ) = μ nigva:rüg;én Xi, i = 1 , 2, …n KW V ( X ) = σ .
i
2
RTwsþIbT 3 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØmanTMhM n
ebI E ( X ) CatémøsgÇwménmFüm X Edltageday μ X eK)an E ( X ) = μ = μ . X
RTwsþIbT 4 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØminGaRs½yman TMhM n
ebI V ( X ) Cava:rüg;én mFüm X Edltageday σ eK)an
2
X V (X ) = σ 2 =
X
σ2
n
.
RTwsþIbT 5 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØGaRs½ymanTMhM n
ebI V ( X ) Cava:rüg;én mFüm X Edltageday σ eK)an V ( X ) = σ = σn ⎛⎜⎝ N −−n ⎞⎟⎠ .
2
X
N 1
2
X
2
σ2
RTwsþIbT 6 ³ ebIsaklsßitimanTMhMGnnþ nigKMrUtagsamBaØGaRs½ymanTMhM n enaHva:rüg;énmFüm X KW σ 2
X
=
n
.
Tung Nget, MSc 6-10

11. 2-bMENgEckKMrUtagkmμénmFümKMrUtag ¬]TahrN_¦
]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.
dMeNaHRsay
KNnamFüménsaklsßiti
Tung Nget, MSc 6-11

12. dMeNaHRsay ¬t¦
Tung Nget, MSc 6-12

13. dMeNaHRsay ¬t¦
eK)an E( X) =μ = ∑⎡X ×p( X = X )⎤ =10 nig
X⎣ i ⎦i V( X) =σ = ∑ i ( )
2
X ⎢
⎣
( )
( i )⎥
⎡ X − E X 2 × p X = X ⎤ =19
⎦
x- krNIKMrUtagécdnüsamBaØGaRs½yeyIg)an ³
eK)an taragbMENgEckKMrUtagénmFüm X nigFatusMxan;² dUcxageRkam ³
20
Tung Nget, MSc 6-13

14. dMeNaHRsay ¬t¦
eK)an E( X) = μ = ∑⎡X × p( X = X )⎤ =10 nig V( X) = σ = ∑⎡( X − E( X)) × p( X = X )⎤ =14.25
X⎣ ⎦ i i
⎢
⎣
2
S i
⎥
⎦
2
i
RTwsþIbT 7 ³ enAkñúgsaklsßitiEdlmanTMhM N nigKMrUtagsamBaØminGaRs½ymanTMhM n enaHsRmab; n FMlμm RKb;RKan; ( n ≥ 30)
σ
eK)anEbgEckmFümKMrUtag X KWRbhak;RbEhl nwgbMENgEckn½rma:l;Edlman mFümnBVnþ μ = μ nigKmøatKMrU σ = n .
X X
bMENgEckén Z = Xσ μ KWRbhak;RbEhl nwgbMENgEckn½rm:al;sþg;dar.
−
X
X
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
σ
μ = μ nigKmøatKMrU σ =
X X
n . bMENgEckén Z = X σ μ KWRbhak;RbEhl nwgbMENgEckn½rm:al;sþg;dar.
−
X
X
RTwsþIbT 9 ³ ebIsaklsßitimanbMENgEckn½rma:l;EdlmanmFüm μ nigKmøatKMrU σ yk n CaTMhMKMrUtagsamBaØ enaHRKb; n ≥ 1
σ
eK)an bMENgEckénmFümKMrUtag X KWmanbMENgEckn½rma:l;EdlmanmFüm μ = μ nigKmøatKMrU σ = n .
X X
bMENgEckén Z = X σ μ KWmanbMENgEckn½rma:l;sþg;dar.
−
X
X
Tung Nget, MSc 6-14

15. 2-bMENgEckKMrUtagkmμénmFümKMrUtag ¬]TahrN_¦
Rkumhu‘nGKÁisnImYyp;litGMBUlePøIgEdlGayurbs;vaRbhak;RbEhl dMeNaHRsay
nwgbMENgEckn½rma:l;EdlmanmFümesμI 800 ema:g nigKmøatKMrU 40 1- X manbMENgEckRbhak;RbEhl nwgr)ayn½rma:l;Edl ³
ema:g. KMrUtagécdnümYymanTMhM 64 GMBUl. μ = μ = 800 nig σ =
σ
=
40
=5
X
n x
64 .
1- cUrKNnaRbU)abedIm,I[GMBUlTaMg 64 enHmanGayukalCamFüm³ k- eK)an P(780 < X < 815) = P(z < Z < z ) Edl ³ 1 2
k- enAcenøaHBI 780 dl; 815 . z =
780 − μ
= 1
780 − 800
X
= −4
σ 5
x- FMCag 785 . 815 − μ
X
815 − 800
z = = X
=3
K- ticCag 775 . σ
2
X
5
P ( 780 < X < 815 ) = P ( −4 < Z < 3)
2- cUrKNnaPaKryénKMrUtagEdlmanGayukalCamFümenAcenøaHBI = P ( −4 < Z < 0 ) + P ( 0 < Z < 3)
785 ema:geTA 810 ema:g. = P ( 0 < Z < 4 ) + P ( 0 < Z < 3)
= 0.49997 + 0.49870 = 0.99867
dUcenH P(780 < Z < 815) = 0.9987 .
775 − μ X 775 − 800
K- eK)an P ( X < 775) = P ( Z < z ) Edl z = σX
=
5
=5
x- eK)an P(X > 785) = P(Z > z) Edl z=
785 − μ X
=
785 − 800
= −3
σX 5
P ( X < 775) = P ( Z < −5) = 0.5000 − P ( 0 < Z < 5) P(X > 785) = P(Z > −3) = 0.5000 + P(0 < Z < 3)
= 0.5000 − 0.4999 = 0.0001 = 0.5000 + 0.4987 = 0.9987
dUcenH P(X < 775) = 0.0001 . dUcenH P(X > 785) = 0.9987 .
Tung Nget, MSc 6-15

16. dMeNaHRsay ¬t¦
⎧ 785 − μ X 785 − 800
⎪ z1 = = = −3
⎪ σX 5
2- eK)an P ( 785 < X < 810) = P ( z < Z < z ) Edl
1 2
⎨
⎪ z = 810 − μ X = 810 − 800 = 2
⎪ 2
⎩ σX 5
P (785 < X < 810 ) = P (− 3 < Z < 2 ) = P (0 < Z < 3) + P (0 < Z < 2 )
= 0.4987 + 4772 = 0.9759
dUcenH PaKryénKMrUtagEdlmanGayukalCamFümenAcenøaHBI 785 ema:geTA 810
ema:gKW 97/59°.
Tung Nget, MSc 6-16

17. 3>bMENgEckKMrUtagkmμénsmamaRt ¬ Sampling distribution of the proportion ¦
eKmansaklsßitimYyEdlmanTMhM N . yk NA CacMnYnFatuénsaklsßitiEdlmanlkçN³ A eKehA ³
p=
N
N
A
faCasmamaRténsaklsßiti ¬Population proportion¦. ecjBIsaklsßitienHeK eRCIserIsKMrUtagécdnüsamBaØmYy
EdlmanTMhM n Edl ³ X1, X2,…Xn-1 nig Xn CatémøEdlTTYl)an. yk XA CacMnYnFatuenAkñúgKMrUtagEdlmanlkçN³ A .
XA
eK)an ³ XA = X1+X2+…Xn nig Ps = faCasmamaRtKMrUtag ¬sample proportion¦.
n
RTwsþIbT 10 ³
- ebIKMrUtagécdnüEdlmanTMhM n enHCaKMrUtagécdnüsamBaØminGaRs½yEdlykecjBIsakl sßitiEdlmanTMhM N b¤ TMhMGnnþenaH
⎧E ( XA ) = np, V ( XA ) = np (1 − p ) , σX = V ( XA ) = np (1 − p )
XA CaGefreTVFa nigeKTaj)anrUbmnþ ³ ⎪
A
⎨ ⎛X ⎞ p (1 − p )
⎪ E ( Ps ) = E ⎜ A ⎟ = p, σPs = V ( Ps ) =
2
, σPs = V ( Ps )
⎩ ⎝ n ⎠ n
- ebIKMrUtagécdnüEdlmanTMhM n enHCaKMrUtagécdnüsamBaØGaRs½yEdlykecjBIsaklsßiti EdlmanTMhM N enaH
⎧ N−n N−n
⎪E ( XA ) = np, V ( XA ) = np (1− p) , σXA = V ( XA ) = np (1− p)
⎪ N −1 N −1
XA CaGefrGuIEBrFrNImaRt nigeKTaj)anrUbmnþ³ ⎨
⎪E ( Ps) = E ⎛ XA ⎞ = p, σ2 = V ( Ps) = V ⎛ XA ⎞ = N − n p (1− p) & σ = σ2
⎪ ⎜ ⎟ Ps ⎜ ⎟ Ps Ps
⎩ ⎝ n ⎠ ⎝ n ⎠ N −1 n
Tung Nget, MSc 6-17

18. 3>bMENgEckKMrUtagkmμénsmamaRt ¬t¦
- ebIKMrUtagécdnüEdlmanTMhM n enHCaKMrUttagécdnüsamBaØGaRs½yEdlykecjBIsaklsßiti
EdlmanTMhMGnnþenaH X CaGefrGuIEBrFrNImaRt nigeKTaj)anrUbmnþ ³
A
⎧E( XA ) = np, V( XA ) = np(1− p) , σX = V( XA ) = np(1− p)
⎪
⎪
A
⎨ ⎛X ⎞ p(1− p) p(1− p)
⎪E( Ps ) = E⎜ A ⎟ = p, σPs = V( Ps) =
2
, σPs = V( Ps) =
⎪
⎩ ⎝ n ⎠ n n
RTwsþIbT 11 ³ enAkñúgsaklsßitiEdlmanTMhM N b¤ Gnnþ nigKMrUtagécdnüEdlmanTMhM n
enHCaKMrUtagécdnüsamBaØminGaRs½ykalNa n kan;EtFMenaHGefrécdnü Z = Pσ− p Edl s
Ps
p (1 − p )
σPs = V ( Ps ) =
n
manbMENgEckRbhak;RbEhlnwgbMENgEckn½rm:al;sþg;dar.
RTwsþIbT 12 ³ enAkñúgsaklsßitiEdlmanTMhM N b¤ Gnnþ nigKMrUtagécdnüEdlmanTMhM n
enHCaKMrUtagécdnüsamBaØGaRs½ykalNa n kan;EtFMenaHGefrécdnü Z = Pσ− p Edl ³ s
Ps
N−n p (1 − p )
σPs = V ( Ps ) =
N −1 n
manbMENgEckRbhak;RbEhl nwgbMENgEckn½rm:al;sþg;dar.
Tung Nget, MSc 6-18

19. ]TahrN_ ³ eKdwgfa 60 ° énGñke)aHeqñatnwge)aHeqñat[KNbkS A. cUrKNnaRbu)abEdl
naM[KMrUtagécdnüsamBaØEdlmanTMhM 160 EdlsmamaRténGñke)aHeqñat[KNbkS A mantic
Cag 50 ° .
dMeNaHRsay
eKman p=60%=0.60 CasmamaRténGñke)aHeqñat[KNbkS A rbs;saklsßiti nig
p CasmamaRtGñke)aHeqñat[KNbkS A rbs;KMrUtagécdnü. eK)an³
s
Ps − p p (1 − p ) 0.60 (1 − 0.60 )
Z=
σ Ps
Edl σ Ps = V ( Ps ) =
n
=
100
= 0.049
Ps − p 0.5 0 − 0.60
Z= = = − 2.04
σ Ps 0.049
deUcH p ( p
ñ s < 0.5 ) = p ( Z < − 2.04 )
= p ( Z > 2.04 )
Tung Nget, MSc 6-19

20. 3>bMENgEckKMrUtagkmμénsmamaRt ¬]TahN_¦
]TahrN_ ³ kñúgcMeNamTMnijTaMg 100 Edl)ansþúkTukman 50 xUc. Pñak;garRtYtBinitü
EdlminsÁal;tYelxenH nwgeRCIserIsykTMnij 15 CaKMrUtagécdnüsamBaØ.
cUrKNnaRbU)abEdlnaM[manTMnijxUceRcInCag 10 TaMgkrNIminGaRs½y nigkrNIGaRs½y.
dMeNaHRsay
CMhanTI1³ rksmamaRténTMnijxUckñúgsaklsßiti k> krNIminGaRs½y ¬eRCIsedaydak;eTAvij¦
nigKMlatKMrUénbMENgEckeTVFa nig eKman smamaRténTMnijxUckñúgsaklsßiti
rk z EdlRtUvKμanwg p = 10.5/15 ¬X+ 0.5
s 0. p=50/100=0.50
KWCaktþaEktRmUvPaBCab;BIeTVFamkn½rma:l;¦ Z=
Ps − p
Edl σ = V ( Ps ) =
p (1 − p )
Ps
σ Ps n
CMhanTI2³ kMNt;épÞcab;BI p = 10.5/15 eLIg.
s 0.50 (1 − 0.50 )
= = 0.1291
15
cMNaM³ kareFVIkMENPaBCab;cMeBaHEtKMrUécdnümanTMhMtUc. Ps − p
10.5
15
− 0.50
Z= = = 1.55
σ Ps 0.1291
Tung Nget, MSc
deUcñH p ⎛ p
⎜
⎝
s >
10.5 ⎞
15 ⎠
⎟ = p ( Z > 1.55 ) = 0.06 1 6-20

21. 3>bMENgEckKMrUtagkmμénsmamaRt ¬]TahN_¦
]TahrN_ ³ kñúgcMeNamTMnijTaMg 100 Edl)ansþúkTukman 50 xUc. Pñak;garRtYtBinitü
EdlminsÁal;tYelxenH nwgeRCIserIsykTMnij 15 CaKMrUtagécdnüsamBaØ.
cUrKNnaRbU)abEdlnaM[manTMnijxUceRcInCag 10 TaMgkrNIminGaRs½y nigkrNIGaRs½y.
dMeNaHRsay
k> krNIGaRs½y ¬eRCIsedaymindak;eTAvij¦
eKman smamaRténTMnijxUckñúgsaklsßiti p=50/100=0.50
Ps − p N−n p (1 − p )
Z=
σ Ps
Edl σ Ps = V (Ps ) =
N −1 n
100 − 15 0 .5 0 (1 − 0 .5 0 )
= = 0 .1 1 9 6
100 − 1 15
1 0 .5
− 0 .5 0
Ps − p 15
Z= = = 1 .6 7
σ Ps 0 .1 1 9 6
dUe cñH p ⎛ p
⎜
⎝
s >
1 0 .5 ⎞
15 ⎠
⎟ = p ( Z > 1 .6 7 )
Tung Nget, MSc 6-21

22. 4> témø)a:n;sμanCacMNuc nigcenøaHTukcitþ ¬ ¦
Point estimates and Confidence intervals
témø)a:a:n;sμan CacMNucCatémøEdlKNna)an BIB½t’manKMrUtag nig
) an
RtUv)aneKeRbIedIm,IeFVICa témø)a:n;sμan)a:ra:Em:Rténsaklsßiti.
Ca]TahrN_ mFümKMrUtag X Catémø)a:n;sμanén mFümsaklsßiti μ cMENk
smamaRtKMrUtag p Catémø)a:n;sμanénsmamaRtsaklsßiti p .
s
cenøaHTukcitþ CacenøaHEdlKNna)anBIB½t’manKMrUtagedIm,I [)a:ra:Em:Rténsaklsßiti sßitenAkñúgcenøaHenH
aHTu
Rtg;RbU)abCak;lak;mYy. RbU)abCak;lak;EdleKR)ab;enH ehAfakRmitTukcitþ ¬Level of confidence¦ .
cenøaHenHehAfatémø)a:n;sμanCacenøaH.
yk θ Ca)a:ra:Em:RtminsÁal;énsaklsßitimYy. ecjBIsaklsßitienH eKeRCIserIsKMrUtagécdnümYyEdl
manTMhM n nigmanGefrécdnü X ,X ,…X nig X bnÞab;mkeKKNna témøsßiti θ minlem¥ógmYyén θ .
1 2 n-1 n
⎧θ − k
⎪
CaeKaleRkam
⎪θ + k CaeKalelI
⎪
eK)an³ ( ) ⎪1 − α
p θ − k ≤ θ ≤ θ + k = 1− α , ⎨
CakRmitTukct
it
⎪θ − k ≤ θ ≤ θ + k:Confidence level X μ
⎪
⎪k CakMhusKrMU
⎪α : Sgnificance
⎩ k
Tung Nget, MSc 6-22

23. 4> karbkRsaytémø)a:n;sμan ¬Interval Estimates- Interpretation¦
cMeBaHcenøaHTukcitþ 95% manRbEhlCa 95% éncenøaHTaMgLayEdlRtUv)ansg; nwgpÞúk)a:ra:Em:tEdl
aHTu aHTaM k)a:
RtUv)a:n;sμan. ehIy 95% énmFümKMrUtagsRmab;TMhMKMrUtagCak;lak;mYy nwgsßitenAkñúgKmøatKMrUén
an. gKmatKM
saklsßitiEdlRtUveFVIetsþ.
sMNakén X
KMrUtag ! TMhM 256 pÞúkmFümsaklsßiti
X1
X2
KMrUtag @ TMhM 256 pÞúkmFümsaklsßiti
KMrUtag # TMhM 256 pÞúkmFümsaklsßiti
X3 KMrUtag $ TMhM 256 pÞúkmFümsaklsßiti
X4
X5
KMrUtag % TMhM 256 minpÞúkmFümsaklsßiti
X6
KMrUtag 6 TMhM 256 pÞúkmFümsaklsßiti
Tung Nget, MSc
mFümsaklsßiti 6-23

24. rebobKNnatémø Z edaysÁl;cenøaHTukcitþ
¬ How to Obtain z value for a Given Confidence Level ¦
cenøaHTukcitþ 95% KWCaEpñkkNþal 95% éntémøGegát.
dUecñH enAsl; 5% RtUvEckCaBIresμIKñarvagcugTaMgsgxag. α (1−α) α
2 2
⎛ ⎞
⇒ p ⎜ 0 < Z < z α ⎟ = 0.4750 tamtarag ⇒ z α = 1.96
⎝ 2 ⎠ 2
tamtarag Appendix B.1. −z α
2
z α
2
⎛ ⎞
p ⎜ −z α < Z < + z α ⎟ = 1 − α
⎝ 2 2 ⎠
cenøa HTuk citþ α zα
α
(1 −α )100% 2 2
90% 0.10 0.05 1.65
95% 0.05 0.025 1.96
99% 0.01 0.005 2.575
Tung Nget, MSc 6-24
0

25. cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIsÁal; σ
cenøaHTukcitþsRmab;mFümsaklsßiti cenøaHTukcitþsRmab;mFümsaklsßiti
edaysÁal; σ KW³ X ± z . σn σ N−n
edaysÁal; σ KW³ X ± z . n ⋅ N −1
α
2
α
2
σ σ
(*) X − zα ⋅ ≤ μ ≤ X + zα ⋅ X − zα .
σ
⋅
N−n
≤ μ ≤ X + zα .
σ
⋅
N−n
2 n 2 n 2 n N −1 2 n N −1
x mFümKMrUtag x mFümKMrUtag
σ KmøatKMrUsaklsßiti σ KmøatKMrUsaklsßiti
N TMhMsaklsßitiminsÁal; N TMhMsaklsßitisÁal;
n cMnYntémøGegátsrubkñúgKMrUtag (>30) n cMnYntémøGegátsrubkñúgKMrUtag (>30)
z témø Z cMeBaHcenøaHTukcitþCak;lak;NamYy z témø Z cMeBaHcenøaHTukcitþCak;lak;NamYy
α α α α
2 2 2 2
1−α 1−α
ebI n/N < 0.05RtUveRbI (*)
X− k
μ
X+ k −zα
2
0
zα
eRBaH N − n → 1
p( X−k <μ< X+k) =1−α
⎛ ⎞ 2
Tung Nget, MSc p ⎜ −z α < Z < +z α ⎟ = 1 − α N −1 6-25
⎝ 2 2 ⎠

26. cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIsÁal; σ ¬]TahrN_¦
mF
]TahrN_³ eKeRCIserIsKMrUécdnücMnYn64)avBIkñúgsaklsßiti)avsIum:g;EdlmFümsaklsßiti μ minsÁal;
ehIymanKmøatKMrU σ = 4KILÚRkam bnÞab;BIføwgrYceKdwgfaTMgn;mFüm X = 48kg edayykcenøaHTukcitþesμI
95% cUrkMnt;cenøaHeCOCak;TMgn;sIum:g;énsaklsßiti ebIKMrUtagécdnüCaKMrUécdnüsamBaØminGaRs½y.
dMeNaHRsay
cenøaHTukcitþsRmab;mFümsaklsßitiKW³
σ 4
X ± zα. = 48 ± z α .
2 n 2 64
1 − α = 0.95 ⇒ z α = z 0.025 = 1.96
α 0.025
2
2
σ 4
X ± zα ⋅ = 48 ± 1.96 × = 48 ± 0.98
2 n 64
⇒ 47.02 ≤ μ ≤ 48.98
Tung Nget, MSc 6-26

27. cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIsÁal; σ ¬]TahrN_¦
mF
]TahrN_³ eKeRCIserIsKMrUécdnücMnYn64)avBIkñúgsaklsßiti)avsIum:g;EdlmFümsaklsßiti μ minsÁal;
ehIymanKmøatKMrU σ = 4KILÚRkam bnÞab;BIføwgrYceKdwgfaTMgn;mFüm X = 48kg edayykcenøaHTukcitþesμI
99% cUrkMnt;cenøaHeCOCak;TMgn;sIum:g;énsaklsßiti ebIKMrUtagécdnüCaKMrUécdnüeRCIseday
mindak;eTAvijBIsaklsßitiTMhM N=1000)av.
dMeNaHRsay
cenøaHTukcitþsRmab;mFümsaklsßitiKW³
σ N−n
N−n
X ± z α ..
zα ⋅⋅
2
2 nn N −1
N −1
1 − α = 0.99 ⇒ z α = z0.005 = 2.575
1 α = 0.99 α = z 0.005 =
2
2
σ N−n 4 1000 − 64
X ± zα . ⋅ = 48 ± 2.575 × = 48 ± 1.24
2 n N −1 64 1000 − 1
⇒ 46.76 ≤ μ ≤ 49.24
Tung Nget, MSc 6-27

28. krNIminsÁal;KmøatKMrUsaklsßiti σ => bMENgEck t
mi al;
enAkñúgsßanPaBeFVIKMrUtag CaFmμta
eKminsÁal;KmøatKMrUsaklsßiti (σ).
lkçN³énbMENgEck t³
1>¦ vaCabMENgEckCab; dUcbMENgEck Edr
Z snμt;Camunfa
2>¦ vamanragCaCYYg nigsIuemRTI dUcbMENgEck Z Edr saklsßitieKarBtamc,ab;nr½ma:l;
3>¦ minEmnCabMENgEck t EtmYyenaHeT EtvaCaRKYsar etIsÁal;KmøatKMrU
énbMENgEck t. bMENgEck t TaMgGs;man mFüm = 0 saklsßitirWeT?
b:uEnþmanKmøatKMrUERbRbYlGaRs½ynwgTMhMénKMrUtag/ n ng n <30 Νο
i Yes rW n > 30
4>¦ bMENgEck t manlkçN³latnigTabenARtg;cMNuckNþalCag cUreRbIbMENgEck t cUreRbIbMENgEck Z
bMENgEcknr½ma:l; EteTaHCaya:gNa bMENgEck t xitCitbMENg C.I : X ± t α .
s
C.I : X ± z α .
σ
n n
Ecknr½ma:l;. 2 2
s N−n σ N−n
C.I : X ± t α . C.I : X ± z α . 6-28
Tung Nget, MSc
2 n N −1 2 n N −1

29. cenøaHTukcitþsRmab;mFümsaklsßitikñúgkrNIminsÁal; σ
mi al;
finite population
correction factor
cenøaHTukcitþsRmab;mFümsaklsßiti cenøaHTukcitþsRmab;mFümsaklsßiti
s s N−n
eRCIsdak;eTAvijKW³ X±t .
n
α
2
eRCIsmindak;eTAvijKW³ X±t .
n
⋅
N −1
α
2
s s s N−n s N−n
(**) X − t α ⋅ ≤ μ ≤ X + tα ⋅ X − tα. ⋅
N −1
≤ μ ≤ X + tα. ⋅
N −1
n n 2 n 2 n
2 2
x mFümKMrUtag x mFümKMrUtag
s KmøatKMrUénKMrUtag s KmøatKMrUénKMrUtag
N TMhMsaklsßitiminsÁal; N TMhMsaklsßitisÁal;
σ KmøatKMrUénsaklsßitiminsÁal; σ KmøatKMrUénsaklsßitiminsÁal;
n cMnYntémøGegátsrubkñúgKMrUtag (<30) n cMnYntémøGegátsrubkñúgKMrUtag (<30)
t témø t cMeBaHcenøaHTukcitþCak;lak;NamYy t témø t cMeBaHcenøaHTukcitþCak;lak;NamYy
α α
α α 2 2
2 2
α α ebI n/N < 0.05RtUveRbI (**)
1− α
2 2
Tung Nget, MSc
eRBaH N − n → 1 6-29
−t
N −1
0
α t α
2 2

30. cenøaHeCOCak;sRmab;μ ¬]TahrN_edayeRbIbMENgEck t¦
]TahrN_³ 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?
1>¦ KNna C.I. edayeRbbMENgEck t ¬eRBaH minsÁaÁ l; σ ¦
edayeRbIb
I mnsa
i
s
s =X±t s
s
X ± t α , n −1 ×
X±t
α
× ×
= X ± t 0.5 , 10−1 ×
2 , n −1 n
n
0.5
2 , 10−1 n
n
2 2
0.09
= 0.32 ± t 0.025, 9 ×
10
0.09
= 0.32 ± 2.262 ×
10
= 0.32 ± 0.064 = [ 0.256, 0.384]
2>¦Tung æaNget, MSc
snñid n³ eragcRkGacR)akdd¾smehtuplfaCeRmARkLa EdlenAsl;CamFümKWenAcenøaHBI 0>@%^ eTA 0>#*$ Gij.6-30

31. cenøaHeCOCak;sRmab; μ
edaymanktþaEktRmUvsaklsßitikMNt; ¬]TahrN_¦
n 40
]TahrN_³ manRKYsarcMnYn @%0 enAkñúg Scandia, eday N
=
250
= 0 .1 6 dUecñHRtUveRbI
Pennsylvania. KMrUtagécdnüTMhM 40 énRKYsar ktþaEktRmUvsaklsþitikMNt;. eKminsÁal;
TaMgenH)an[dwgfa karbricakcUlkñúgRBHviha KmøatKMrUsaklsßiti KUeRbIbMEM NgEck t Et n>30
b
RbcaMqñaMKWesμI $450 nigKmøatKMrUénKMrUtagenHKW $75. => eRbIbMENgEck Z .
etImFümsaklsßitiGacesμI $445 rW $425 EdrrWeT? X±z
α
2
s N−n
n N −1
= $450 ± z
0.05
$75 250 − 40
40 250 − 1
etImFümsaklsßitiesμInwgb:unμan? = $450 ± 1.65
$75 250 − 40
40 250 − 1
rktémø)a:n;sμan 90% sRmab;mFümsaklsßiti. = $450 ± $19.57 0.8434
tambRmab;³ N = 250 = $450 ± $18 = [$432, $468]
n = 40
s = $75
mFümsaklsßitiTMngCaFMCag $432 b:unEnþ tUcCag $468.
mFümsaklsßitiGacesμI $445 b:uEnþ minesμI $425eT eRBaH $445
Tung Nget, MSc
sßitenAkñúgcenøaHTukcitþ cMENk $425 minenAkñúgcenøaHenHeT.6-31

32. finite population
cenøaHTukcitþsRmab;smamaRtsaklsßitikñúgkrNIsÁal; σ
al; correction factor
cenøaHTukcitþsRmab;smamaRtsaklsßiti cenøaHTukcitþsRmab;smamaRtsaklsßiti
smamaRtsakls smamaRtsakls
Ps (1 − Ps ) Ps (1 − Ps ) N − n
eRCIsdak;eTAvijKW³ Ps ± z n α
2
eRCIsmindak;eTAvijKW³ Ps ± z
n N −1
α
2
Ps (1 − Ps ) Ps (1 − Ps ) Ps (1 − Ps ) N − n Ps (1 − Ps ) N−n
Ps − z α ≤ p ≤ Ps + z α Ps − z α ≤ p ≤ Ps + z α
2
n 2
n 2
n N −1 2
n N −1
ps smamaRtKMrUtag (***) ps smamaRtKMrUtag
N TMhMsaklsßitiminsÁal; N TMhMsaklsßitisÁal;
σ KmøatKMrUénsaklsßitisÁal; σ KmøatKMrUénsaklsßitisÁal;
n cMnYntémøGegátsrubkñúgKMrUtag (>30) n cMnYntémøGegátsrubkñúgKMrUtag (>30)
Zα témø Z cMeBaHcenøaHTukcitþCak;lak;NamYy
α
Zα témø Z cMeBaHcenøaHTukcitþCak;lak;NamYy
α
2 2 2 2
⎛ ⎞
p ⎜ −z α < Z < + z α ⎟ = 1 − α
α
2
1− α
α
2
ebI n/N < 0.05RtUveRbI (***)
⎝ 2 2 ⎠
Tung Nget, MSc −z z
eRBaH N − n → 1 6-32
α
2 0
α
2
N −1

33. cenøaHTukcitþsRmab;smamaRtsaklsßiti ¬]TahrN_¦
]TahrN_³ shKmtMNag[ BBA kMBugBicarNa dMeNaHRsay
elIsMeNIrbBa¢ÚlKñaCamYy Teamsters Union. dMbg/ KNnasmamaRténKMrUtag:
U
eyagtamc,ab;shKm BBA ya:gehacNas; 3/4 x 1,600
énsmaCikPaBshKm RtUvEtyl;RBmcMeBaH kardak; ps = =
n 2000
= 0.80
bBa©ÚlKña. KMrUtagécdnüénsmaCik BBA bc©úb,nñcMnYn KNna 95% C.I.
ps (1 − ps )
@/000nak; )an[dwgfa !/^00nak; manKeRmage)aH C.I. = ps ± z α / 2
n
eqñatKaMRTsMeNIrbBa©ÚlKñaenH. = 0.80 ± 1.96
0.80(1 − 0.80)
= 0.80 ± 0.018
cUrKNnasmamaRtsaklsßiti. = [ 0.782, 0.818]
2,000
cUrsg;cenøaHTukcitþ 95% sRmab;smamaRtsaklsßiti. snñidæan³ sMeNIrdak;bBa©ÚlKñanwgTMngCaGnum½t)an
edayEp¥kelIkarseRmccitþrbs;Gñk elIB½t¾mankñúg eRBaHenøaH)a:n;sμanpÞúktémøFMCag énsmaCikPaB.
75%
KMrUtag etIGñkGacsnñidæanfasmamaRtcaM)ac;énsmaCik
BBA eBjcitþcMeBaHkarbBa©ÚlKñaEdrrWeT? ehtuGVI?
Tung Nget, MSc 6-33
0

34. cenøaHTukcitþsRmab;smamaRtsaklsßiti ¬]TahrN_¦
dMeNaHRsay
]TahrN_³ k> dMbUg/ KNnasmamaRténKrMUtag:
shRKasplitkg;LanmYyplitkg;LanCaeRcIn. x
edIm,IBinitüemIlPaBsViténkg;LangTaMgenaH eKeRCIs n p = = 0.10
s
edayécdnünUvkg;LancMnYn n=50 CaKMrUtagécdnü. KNna 95% C.I.
eKGegáteXIjfamankg;Lan 10% mineqøIytbnwg C.I. = p ± z p (1n− p )s α/2
s s
sMNUmBr. cUrkMNt;cenøaHTukcitþ sRmab;smamaRt p = 0.10 ± 1.96 0.10(1 − 0.10) = 0.10 ± 0.083
énkg;LanTaMgGs;EdlplitmintamsMNUmBr eday 50
ykkMritTukcitþ 95% ebI³ x
x> dMbUg/ KNnasmamaRténKrMUtag p = n = 0.10
k> KMrUtagCaKMrUtagminGaRs½y. KNna 95% C.I.
s
x> KMrUécdnüCaKMrUécdnüeRCIsmindak;eTAvij p (1− p ) N − n
nigLanEdlplitTaMgGs;mancMnYn 400kg;. C.I. = p ± z
s α/2
n
s s
N −1
0.10(1− 0.10) 400 − 50
= 0.10 ±1.96
50 400 −1
= 0.10 ± (1.96×0.04) = 0.10 ± 0.0784 = [0.0218, 0.1784]
Tung Nget, MSc 6-34
0

35. kareRCIserIsTMhMKMrUtagd¾smRsb
manktþa 3ya:gEdlkMNt;TMhMKMrUtag EdlKμanktþa ]TahrN_³
NamYymanTMnak;TMngedaypÞal; cMeBaHTMhM nisSitenAkñúgrdæ)alsaFarNcg;kMNt;brimaN
saklsßitieT. mFümEdlsmaCikénRkumRbwkSaRkugkñúg
1.) kMritTukcitþEdlcg;)an TIRkugFM² rkcMNUl)ankñúgmYyExBIkareFVICa
2.) kMritel¥ógEdlGñkRsavRCavnwgTTYyk)an smaCik. kMhuskñúg kar)a:n;sμanmFümKWRtUv
3.) karERbRbYlkñúgsaklsßitiEdlkMBugRtUvsikSa tUcCag $100 edaymancenøaHTukcitþ 95%.
⎛ z ⋅σ ⎞
2 nisSitenaH)anrkeXIjfar)aykarN_eday
n =⎜α/2
⎝ E ⎠
⎟ naykdæankargarEdl)an)a:n;sμanBIKmøatKMrUKW
RtUvesμI $1,000. etIeKRtUvkareRCIserIsTMhM
Edl ³ n TMhMKMrUtag KMrUtagEdlRtUvkarb:unμan?
zα/2 Catémønr½ma:l;KMrUEdlRtUvKñanwgkMrit dMeNaHRsay
TukcitþEdlcg;)an n =⎜
⎛z α/2 ⋅σ ⎞
2
⎟
⎝ E ⎠
σ KmøatKMrUsaklsßiti 2
⎛ (1 .9 6 )($ 1, 0 0 0 ) ⎞
E kMhusEdlGacGnuBaØat[manFMbMput =⎜ ⎟ = (1 9 .6 )
2
Tung Nget, MSc ⎝ $100 ⎠ 6-35
0
= 3 8 4 .1 6 = 3 8 5

36. kareRCIserIsTMhMKMrUtagedIm,I)a:n;sμansmamaRtsaklsßiti
2
]TahrN_³
n = p(1 − p) ⎜
⎛ Zα / 2 ⎞ køib American Kennel Club cg;)a:n;sμansmamaRt
⎝ E ⎟ ⎠ énekμgEdlmanEqáCastVciBa©wm.RbsinebIkøwbenHcg;
Edl ³ )ankar)a:n;sμanEdlRtUvCamYy 3% énsmamaRt
n TMhMKMrUtag
saklsßiti etIBYkeKRtUvTak;TgsmÖasn_ekμg²cMnYn
b:unμannak;? snμt;cenøaHTukcitþesμI 95% ehIykøwbenH
zα/2 Catémønr½ma:l;KMrUEdlRtUvKñanwgkMrit )an)a:n;sμanfa 30%énekμg²manEqáCastVciBa©wm.
TukcitþEdlcg;)an 2
dMeNaHRsay n = (0.30)(0.70) ⎛ 1.96 ⎞ = 897
⎜ ⎟
σ KmøatKMrUsaklsßiti ⎝ 0.03 ⎠
E kMhusEdlGacGnuBaØat[manFMbMput ]TahrN_³
0 karsikSamYyRtUvkar)a:n;sμanBIsmamaRténTIRkug
cMNaM³ ebIKμanB½t¾manGMBIRbU)abénPaB EdlmanGñkcak;sMramÉkCn. GñkGegátcg;)an
eCaKC½y eyIgyk p = 0.5. kRmitkMhusRtUvCamYy 0.10 énsmamaRtsakl
2
⎛ 1.65 ⎞ sßiti nigkRmitTukcitþKWesμI 90 PaKry ehIyKμan
n = (`0.5)(1 − 0.5) ⎜ ⎟ = 68.0625 kar)a:n;sμanNamYysþIGMBIsmamaRtsaklsßitieT.
⎝ 0.10 ⎠
n = 69 TRkg
I u
Tung Nget, MSc etIeKRtUvakarTMhMKMrUtagb:unμan? 6-36

37. cb;edaybribUN_
GrKuNcMeBaHkarykcitþTukdak;¡
rrr<sss
Tung Nget, MSc 6-37