1. CMBUkTI 7
kareFVIetsþsmμtikmμelIKMrUtagmYy
ti elI
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 7-1
2. kareFVIetsþsmμtikmμelIKMrUtagmYy
• vtßúbMNg³ enAeBlEdlGñkbBa©b;enAkñúgCMBUkenH GñknwgGac³
1. kMNt;niymn½yénsmμtikmμ nigkareFVIetsþsmμtikmμ
2. BiBN’naBIdMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
3. EbgEckBIPaBxusKñarvagetsþsmμtikmμmçag nigetsþTaMgsgxag
4. eFVIetsþsmμtikmμelImFüm/ krNIsÁal;KmøatKMrUsaklsßiti ebI n ≥ 30
5. eFVIetsþsmμtikmμelImFüm/ krNIminsÁal;KmøatKMrUsaklsßiti ebI n ≥ 30
6. eFVIetsþsmμtikmμelImFüm/ krNIminsÁal;KmøatKMrUsaklsßiti ebI n < 30
7. eFVIetsþsmμtikmμelIsmamaRtsaklsßit
Tung Nget, MSc 7-2
3. kareFVIetsþsmμtikmμμelIKMrUtagmYy
1-smμtikmμ nigkareFVIetsþsmμtikmμ
2> dMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
3-cMnucsMxan;edIm,IcgcaMBI H nig H
0 1
4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30
6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30
7-eFVIetsþsmμtikmμsRmab; p
Tung Nget, MSc 7-3
4. 1-smμtikmμ nigkareFVIetsþsmμtikmμ
(Hypothesis and Hypothesis Testing)
smμtikmμCaBuMenalGMBItémøén)a:ra:Em:Rtsaklsßiti EdleK)anbegáItsRmab;eKalbMNgénkareFVIetsþ.
kareFVIetsþsmμtikmμCadMeNIrkarmYy ¬edayBwgEp¥kelI PsþútagKMrUsak nigRTwsþIRbU)ab¦ EdlRtUv)aneKeRbI
ti
edIm,IkMNt;faetIsmμtikmμenaHCaBMuenalRtwmRtUvEdrb¤eT?
2> dMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
TI2 TI3 TI4
eRCIserIsyk KNnaetsþ
KNnaetsþsßiti begáItviFanén
RbU)ab‘ÍlIetRcLM karseRmccitþ
TI1 minbdiesFsmμtikmμsUnü (H0)
TI5
kMNt;smμtikmμsUnü (H0)
eFVIkarseRmccitþ
nigsmμtikmμqøas; (H1)
bdiesFsmμtikmμsUnü (H0)
nigTTYlyksmμtikmμqøas; (H1)
Tung Nget, MSc 7-4
5. 2> dMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
CMhanTI1³ kMNt;smμtikmμsUnü (H ) nigsmμtikmμqøas; (H ) ³
0 1
-smμtikmμsUnü (H ) KWCaGMNHGMNagGMBItémøén)a:ra:Em:Rtsaklsßiti.
0
-smμtikmμqøas; (H ) KWCaGMNHGMNagEdlRtUveKTTYlebITinñn½yKMrUsakpþl;nUv
1
PsþútagRKb;RKan;fasmμtimμsUnüminRtwmRtUv.
CMhanTI2³ RbU)abRcLM ¬The level of significance¦
CaRbU)abEdlbdiesdsmμtikmμsUnü enAeBlEdl smμtikmμsUnüRtwmRtUv.
- kMhusRbePT I³³ bdiesd H enAeBlEdl H RtwmRtUv.
I
- kMhusRbePT II³ TTYlyk H enAeBlEdl H minRtwmRtUv.
0 0
0 0
CMhanTI3³ KNnasßitietsþ.
sßitietsþ³ CatémøkMNt;BIB½t’manKMrUtag nigRtUveKeRbIedIm,IkMNt;faetIRtUv
TTYlyk b¤bdiesdsmμtisUnü.
Tung Nget, MSc 7-5
6. 2> dMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
CMhanTI4³ begáItviFanénkarseRmccitþ.
témøvinicä½y³ CacMNucx½NÐrvagEdnEdlsmμtikmμsUnüRtUbveKbdiesd nigEdnEdlsmμtikmμ
(Critical value)
sUnüminRtUveKbdiesd.
CMhanTI 5 eFVIkarseRmccitþ edayBwgEpñkelIB½t’manBIKMrUsak eyIgeFVIkarseRmccitþfa
etIRtUvbdiesdsmμtikmμsUnü b¤ k¾minbdiesd.
témøvinicä½y³(Critical value)
Tung Nget, MSc 7-6
7. 3-cMnucsMxan;edIm,IcgcaMBI H0 nig H1
• H0 : smμtikmμsUnü nig H : smμtikmμqøas;
1
• H0 nig H KWmincuHsRmugKña nigTUlMTUlaybMput
1
BaküKnøw nimitþsBaØa Epñkén
• H0 : EtgEtRtUvsnμt;faBit
• H1 : CabnÞúkRtUvbkRsay FMCag ¬rWeRcInCag¦ > H 1
• KMrUtagécdnüTMhM (n) RtUveRbIedIm,I {bdiesF H }
• RbsinebIsnñidæanfa{minbdiesF H } karenHminEmn
0
tUcCag < H 1
0
mann½yfa H BitenaHeT b:uEnþRKan;EtesñIfaKμansmμtikmμ
0
mineRcInCag ≤ H 0
RKb;Rkan; edIm,IbdiesF H ehIykarbdiesF H
0 0 ya:gehacNas; ≥ H 0
mann½yfasmμtikmμqøas;GacBit. )anekIneLIg > H
• smPaBCaEpñkén H (e.g. “=” , “≥” , “≤”).
1
0
• “≠” “<” nig “>” CaEpñkén H 1
etImanPaBxusKñarWeT? ≠ H 1
• kñúgkarGnuvtþ sßanPaBbc©úb,nñRtUvkMNt;Ca H
0
min)anpøHbþÚr = H 0
• RbsinebIkarGHGagmYy{RbkbedayemaTnPaB} {rIkcMerIn}/{RbesICagmun} H1
enaHkarGHGagenHRtUvkMNt;Ca H ¬{cUrbgðajxJúM{¦
1
• kñúgkaredaHRsaybBaða cUrrkemIlBaküKnøwehIy bMElg ⎧ H o : μ = 100
⎨
⎧H o :p = 0.95
⎨
⎩ H1 : μ ≠ 100 ⎩H1 :p ≠ 0.95
vaCanimitþsBaØa. BaküKnøwmYycMnYndUcCa³ ⎧ H o : μ ≤ 100 ⎧H o : p ≤ 0.95
rIkcMerInCagmun/ xusBI/ )anpøHbþÚr/ manRbsiTßdUc.l. ⎨
⎩ H1 : μ > 100
⎨
⎩H1 : p > 0.95
Tung Nget, MSc ⎧ H o : μ ≥ 100 ⎧ H o :p ≥ 0.95 7-7
⎨ ⎨
⎩ H1 : μ < 100 ⎩H1 :p < 0.95
8. 4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30
⎧H o :μ = μ 0 ⎧H o :μ ≥ μ 0 ⎧H o :μ ≤ μ 0
⎨ ⎨ ⎨
⎩H1 :μ ≠ μ 0 ⎩H1 :μ < μ 0 ⎩H1 :μ > μ 0
bdiesd H ebI³ 0 bdiesd H ebI³0 bdiesd H eb³
I 0
Z > Zα 2 Z < − Zα Z > Zα
x−μ
Z=
σ
n
Tung Nget, MSc 7-8
9. 4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_³ Rkumh‘un Jamestown Steel plitnigdMeLIgtu nigeRKOgbrikça
kariyal½ydéTeTot. plitplRbcaMs)þah_éntuKMrU A325 enAÉeragcRk
Fredonia Plant eKarBtam bMENgEckRbU)abnr½ma:l; EdlmanmFümesμI 200 nig
KmøatKMrUesμI16. fμI²enHviFIsaRsþplitfμIRtU)anykmkeRbI ehIykmμkrfμI RtUv)anCYl.
GnuRbFanRkumh‘uncg;GegátemIlfaetImankarpøHbþÚrkñúgkarplitRbcaMs)aþh_éntuKMrU
A325 Edr rIeTedayeRbIRbU)abRcLM α = 0.01 . cMnYntumFümRbcaMs)aþh_Edlplit
qñaMmunesμI 203.5 ¬BIKMrUtag50s)aþh_eRBaH eragcRkbitTVar 2 s)aþh_eBlvismkal¦.
CMhan 1 kMNt;smμtikmμsUnü (H ) nigsmμtikmμqøas; (H )
0 1
CMhan 3 eRCIserIsetsþsßitieRbIbMENgEck
H0: μ = 200
H1: μ ≠ 200 Z-distribution eRBaHsÁal; σ
(kMNt;sMKal;³ BaküKnøwH {mankarpøHbþÚr}) CMhan 4 begáItviFanénkarseRmccitþ³
CMhan 2 eRCIserIsRbU)abkMhus bdiesF H RbsinebI | Z| > Zα/2
0
Tung Nget, MSc 7-9
α = 0.01 dUcmankñúglMhat;
10. 4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
Z > Zα / 2
X −μ
> Zα / 2
σ/ n
203.5 − 200
> Z0.01/ 2
16/ 50
1.55 mnFMCag 2.58
i
CMhanTI 5 eFVIkarseRmccitþnigbkRsay³
edaysar !>%% minFøak;kñúgtMbn;e)aHbg;ecal enaH H minRtUvbdiesFecaleT.
0
eyIgGacsnñidæanfamFümsaklsßitiminxusBI @00eT.
dUecñHeyIgKYraykarN_eTAGnuRbFanEpñkplitfaPsþútagKMrUtagminbgðajfa
GRtaplitenAÉeragcRkmankarpøHbþÚrBI @00 kñúgmYys)aþh_ eT.
Tung Nget, MSc 7-10
11. 4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ KMrUsakmYyEdlmanTMhM 36 RtUveKeRCIserIsedayécdnüecjBIsakl sßitin½rma:l;.
eK[mFümKMrUKMrUsakesμInwg 21 nigKmøatKMrUsaklsßitiesμInwg 5 .
cUreFVIetsþ smμti kmμ H :μ ≤ 20, H : μ > 20 edayeRbIRbU)abRcLM α = 0.05 .
o 1
dMeNaHRsay
CMhanTI 1 ³ smμtikmμsUnü nigsmμtikmμqøas;KW³
⎧ H o :μ ≤ 20
⎨
⎩H 1 ;μ > 20
CMhanTI 2 ³ RbU)abRcLM α = 0 . 05
CMhanTI 3 ³ sßitietsþKW z = σx /− μn
CMhanTI 4 ³ tamtaragcMeBaH α = 0 . 05 eK)an Z = 1 . 65 .
0 . 05
TTYlyk H ebI z ≤ 1 . 65 nigbdiesd H ebI z > 1 . 65 .
o o
sUmemIlrUbTI 4 .
21 − 20
CMhanTI 5 ³ z=
5
= 1.2 eday z = 1.2 < 1.65 enaHeKTTYlysmμtikmμsUnüRtg;
36
Tung Nget, MSc RbU)abRcLM 0.05 . 7-11
12. 4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ Rkumhu‘nRsaebormYy)anGHGagfa cMNuHRsaeborCamFümkñúgmYykMbu:g² eRcInCagrWesμInwg
330 ml . edIm,IFana)annUvkarGHGagenH eK)aneRCIserIsRsaeborcMnYn 64kMbu:g EdleKdak;lk;enAelI
TIpSaredayécdnü nigeXIjfa CamFümkñúg 1 kMbu:g mancMNuH 327ml . KmøatKMrUsaksßitiesμInwg 5 ml .
cMNuHRsaebormanbMENgEckn½rma:l;. edayeRbIRbU)abRcLM α = 0.05 etIkarGHGagenHBitb¤eT?
dMeNaHRsay
CMhanTI 1 smμtikmμsUnü nigsmμtikmμqøas;KW ³
⎧ H o :μ ≥ 330
⎨
⎩ H 1 :μ < 330
CMhanTI 2 RbU)abRcLM α = 0 . 05
CMhanTI 3 sßitietsþKW z = x − μ σ
n
CMhanTI 4 tamtaragcMeBaH α = 0 . 05 eK)an z = 1 . 65 . 0 . 05
TTYlyk H ebI z ≥ − 1 . 65 nigbdiesd H ebI z < − 1 .6 5 . sUmemIlrUbTI 5 .
o o
CMhanTI 5 ³ z = 3 2 7 − 3 3 0 = − 4 .8 . eday z = − 4 . 8 < − 1 . 65 enaHeKminTTYlyksmμti
5
64
Tung Nget, )abRcLM 0.05 eT.
kmμsUnüRtg;RbUMSc dUecñH karGHGagenHminBiteT. 7-12
13. 4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ KMrUsakmYyEdlmanTMhM 49 RtUveKeRCIserIsedayécdnüecjBIsaklsßiti n½rma:l; .
mFümKMrUsak esμInwg 18 nigKmøatKMrUsaklsßitiesμInwg 5 . cUreFVIetsþ smμtikmμ
H : μ = 20, H : μ ≠ 20 ebI z ≥ −1.65 edayeRbIRbU)abRcLM α = 0.10 .
o 1
dMeNaHRsay
CMhanTI 1 ³ smμtikmμsUnü nigsmμtikmμqøas;KW ³
H o : μ = 20
H 1 : μ ≠ 20
CMhanTI 2 ³ RbU)abRcLM α = 0.10
CMhanTI 3 ³ sßitietsþKW z = σx /− μn
CMhanTI 4 ³ tamtaragcMeBaH α = 0.10 eK)an z = 1 .65 . TTYlyk H ebI
0 . 05 o
− 1 . 65 ≤ z ≤ 1 . 65 nigbdiesd H ebI z ≥ 1.65 . emIlrUbTI 6.
o
CMhanTI 5 ³ z = 18/ − 49 = −2.8 . eday z = −
5
20
2.8 < − 1 .65 enaHeKminTTYlyksmμtikmμ
sUnüRtg;RbU)abRcLM 0.10 eT.
Tung Nget, MSc 7-13
14. 5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30
⎧H o :μ = μ 0 ⎧H o :μ ≤ μ 0 ⎧H o :μ ≥ μ 0
⎨ ⎨ ⎨
⎩H1 :μ ≠ μ 0 ⎩H1 :μ > μ 0 ⎩H1 :μ < μ 0
bdiesd H ebI³0 bdeisd H eb³
0I bdiesd H ebI³0
z > zα 2 z > zα z < −zα
KMrUtagminGaRs½y
x − μ0 ⎪
³dWeRkesrI
⎧n − 1
z= , n ≥ 30
s ⎪x³mFümKMrUt ag
⎪
n
Edl ³mFümsaklsßit iEdlRtUveFeIVtsþ
⎪μ
⎪
⎨
KMrUtagGaRs½y ³KMl aKrM UénKrMUt ag
⎪s
⎪
z=
x − μ0
, n ≥ 30
³cMnYnéntémG egát kñug KMrUt ag
⎪n ø
⎪
N−n
×
s ³TMh Ms aklsßt i
⎪N
⎩ i
N −1 n
Tung Nget, MSc 7-14
15. 5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦
]TarhN_ ³ ma:suInqugkarehVsV½yRbvtþmYy RtUv)anGñklk;bBa¢a[qugmYyEBgcMNuHmFüm 25 cl
edayman KMlatKMrUminsÁal; b:uEnþedaymanBaküriHKn;BIGñkTTYlTankaehVfacMNuHkarehVminRKb;
Gñklk;)an[ma:suIn enaHqug 100EBg CaKMrécdnü ehIyKNna)ancMNuHmFüm 24.2cl nig KMlatKMrU
U
1.5cl etIGñklk;vinicä½yya:g NacMeBaHBaküriHKn;enaH edayyk α = 5% .
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
H0: μ ≥ 25cl
H1: μ < 25cl
CMhan 2³ RbU)abRcLM α = 0.05
x −μ
CMhan 3³ sßitietsþ z = 0
eRBaHminsÁal; σ
Tung Nget, MSc
s/ n 7-15
16. 5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦
CMhan 4³ BaküriHKn;rbs;GñkTTYlTankarehVBit ¬bdiesF H0¦
ebI z < -zα
α = 5% ⇒ P ( Z > z 0.05 ) = 0.05 ⇔ P (0 < Z < z 0.05 ) = 0.45
⇒ z 0.05 = 1.645
CMhan 5³ seRmccitþnigbkRsaycemøIy³
X −μ0 24.2 − 25
z= = = −5.33 ⇒ z = −5.33 < −z0.05 = −1.645
S/ n 1.5
100
)ann½yfa bdiesF H0
mann½yfaBaküriHKn;rbs;GñkTTYlTankaehVBit .
Tung Nget, MSc 7-16
17. 5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ Rkumhu‘nRsaebormYy)anGHGagfa cMNuHRsaeboCamFümkñúgmYy²kMbu:g² esμInwg 330ml
edIm,IFana)annUvkarGHGagenH eK)aneRCIserIsRsaeborcMnYn 36 kMbu:g EdleKdak;lk;enAelITIpSareday
écdnü nigeXIjfaCamFmükñúg 1 kMbu:gmancMNuH 328ml nigKmøatKMrUKMrUsakenHesμI nwg 8ml .
cMNuHRsaebormanbMENgEckn½rma:l;. edayeRbIRbU)abRcLM α = 0.05 etIkarGHGagenHBit b¤eT ?
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
H0: μ = 330ml
H1: μ ≠ 330ml
CMhan 2³ RbU)abRcLM α = 0.05
CMhan 3³ sßitietsþ
Tung Nget, MSc
z=
x − μ0
s eRBaHminsÁal; σ 7-17
n
18. 5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦
CMhan 4³ bdiesF H0 ebI z > zα / 2
α
α = 0.05 ⇒ = 0.025 => P(Z > z0.025 ) = 0.025
2
⇔ P(0 < Z < z0.025 ) = 0.475 ⇒ z0.025 =1.96
CMhan 5³ seRmccitþnigbkRsaycemøIy³
x − μ 0 328 − 330
z=
s
=
8
= −1.5 ⇒ z = −1.5 minFCag z
M 0.025 = 1.96
n 36
)ann½yfa TTYlyk H0 mann½yfa karGHGagenHBit
Tung Nget, MSc 7-18
19. 6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30
enAeBlEdlKmøatKMrUsaklsßiti (σ) minsÁal; enaHKmøatKMrU (s)énKMrUtagRtUveRbICMnYs
vij ehIybMENgEck t RtUveRbICaetsþsßitiEdlKNnatamrUbmnþxageRkam³
⎧H o :μ = μ 0 ⎧H o :μ ≤ μ 0 ⎧H o :μ ≥ μ 0
⎨ ⎨ ⎨
⎩H1 :μ ≠ μ 0 ⎩H1 :μ > μ 0 ⎩H1 :μ < μ 0
bdeisd H ebI³ 0 bdeisd H ebI³ 0 bdeisd H ebI³ 0
t > tα 2, n −1 t > t α , n −1 t < − t α , n −1
KMrUtagminGaRs½y KMrUtagGaRs½y ³dWeRkesrI
⎧n − 1
⎪
³mFümKMrtag
⎪x U
x − μ0 x − μ0 ⎪
t=
s
, n < 30 t =
N−n s
, n < 30
Edl ³mFümsaklsitEidlRtveFeIVtsþ
⎪μ
⎪
⎨
ß U
n
× ³KlatKMrUénKrMtag
⎪s M U
N −1 n ⎪
³cMnYnéntémGegátkñugKMrUtag
⎪n ø
⎪
Tung Nget, MSc ⎩³TMhMsaklsßti
⎪N i 7-19
20. 5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
]TahrN_³
EpñkTamTarRkumh‘unFanara:b;rg McFarland raykarN_faéføcMNaymFüm edIm,IdMeNIr
karTamTarKW $60. kareRbobeFob]sSahkmμ)anbgðajfabrimaNenHFMCagRkumh‘unFana
ra:b;rgdéTeTot dUecñHRkumh‘unbegáItrgVas;kat;bnßyéfø. edIm,IvaytémøBIplb:HBal;én
rgVas;kat;bnßyéføenH GñkRKb;RKgEpñkTamTar)aneFVIkareRCIerIsKMrUtagécdnüénkarTamTar
TMhM @^ Edl)andMeNIrkarkalBIExmun. B½t¾manBIKMrUtagmandUcxageRkam.
edayeRbIRbU)abRcLM = 0>0! etIvasmehtuplrWeTEdlfakarRbkasLÚvenHKWticCag $60?
Tung Nget, MSc 7-20
21. 5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
H0: μ ≥ $60
H1: μ < $60
CMhan 2³ RbU)abRcLM α = 0.01
CMhan 3³ sßitietsþ t = sx/ − μ eRBaHminsÁal; σ
n
CMhan 4³ bdiesF H RbsinebI t < -tα,n-1
0
CMhan 5³ seRmccitþnigbkRsaycemøIy³
x − μ $56.42 − $60
t= = = −1.818
s / n $10.04 / 26
eday -!>*!* minFøak;kñúgtMbn;bdiesF enaH H minRtUv
0
bdiescMeBaHRbU)abRcLM 0>0! eT. eyIgmin)anbgðaj
fargVas;kat;bnßyéfø)anbnßyéføcMNaymFümkñúgkar
TamTar[TabCag $60eT. PaBxusKñacMnYn $3.58
($56.42-$60) rvagmFümKMrUtagnigmFümsaklsßiti
GacbNþalmkBIkMhuskñúgkareFVIKMrUtagkmμ.
Tung Nget, MSc 7-21
22. 6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
]TahrN_ ³ rdækrTwkmanGagsþúkTwksMrab;pÁt;pÁg;TIRkugmYy EdleRbIR)as;)anRKb;RKan;kalNaRKYsar nImYy²
kñúgTIRkugenaHmansmaCikCamFüm 5 nak; . eday)armμN_xøacmankarxVHxatTwk EdlRtUvpÁg;eKeRCIserIs 16
RKYsarkñúgTIRkugenaH CaKMrUécdnüGegátrkedIm,IGegátrkcMnYnsmaCikRKYsarCamFüm . eRkayGegáteKKNna
)ancMnYnsmaCikCamFümkñg KMrUécdnü X = 5.038 nak; . edaysnμt;faKMlatKMrUsßiti S = 0.1nak;
etIrdækrTwkvinicä½yya:gNa? edayyk α = 5% .
k-krNIKMrUécdnüsamBaØminGaRs½y
x-krNIKMrUécdnüsamBaØeRCIsmindak;eTAvij ebIkñúgTIRkugenaHman 200 RKYsar .
k-krNIKMrUécdnüsamBaØminGaRs½y
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
H0 : μ ≤ 5
H1 : μ > 5
CMhan 2³ RbU)abRcLM α = 0.05 7-22
Tung Nget, MSc
23. 6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
x − μ0
CMhan 3³ sßitietsþ t=
s/ n
eRBaHminsÁal; σnig n<30
CMhan 4³ karpÁt;pÁg;TwknwgxVH ¬bdiesF H0¦ ebI t > tα, n-1
bMENgEck Student dWeRkesrI n-1=15 tamtMélRbU)ab‘ÍlIet
0.05 eK)an³
t α , n − 1 = t 0 .0 5 , 1 5 = 1 .7 5 3
CMhan 5³ seRmccitþnigbkRsaycemøIy³
X −μ0 5.03− 5
t=
S/ n
=
0.1
=1.2 ⇒ t =1.2 minFCag t
M 0.05, 15 =1.753
16
)ann½yfa TTYlyk H0 mann½yfa smaCikRKYsarCamFümmin
eRcInCag 5 nak;eT ehIyrdækrBuMmankar)armμN_faxVHxatTwkpÁt;pÁg;
kñúgTIRkugeT.
Tung Nget, MSc 7-23
24. 6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
x-krNIKMrUécdnüsamBaØeRCIsmindak;eTAvij ebIkñúgTIRkugenaHman
200 RKYsar .
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
H0 : μ ≤ 5
H1 : μ > 5
CMhan 2³ RbU)abRcLM α = 0.05
x − μ0
CMhan 3³ sßitietsþ t=
N−n
×
s
eRBaHminsÁal; σ nig n<30
N −1 n
Tung Nget, MSc 7-24
25. CMhan 4³ karpÁt;pÁg;TwknwgxVH ¬bdiesF H0¦ ebI t > tα, n-1
bMENgEck Student dWeRkesrI n-1=15 tamtMélRbU)ab‘ÍlIet 0.05
eK)an³ t α, n −1 = t 0.05, 15 = 1.753
CMhan 5³ seRmccitþnigbkRsaycemøIy³
x − μ0 5.03 − 5
t=
N−n s
=
200 − 16 0.1
= 1.25 ⇒ t = 1.25 minFCag t
M 0.05, 15 = 1.753
× ×
N −1 n 200 − 1 16
)ann½yfa TTYlyk H0 mann½yfa smaCikRKYsarCamFümmin
eRcInCag 5 nak;eT ehIyrdækrBuMmankar)armμN_faxVHxatTwkpÁt;pÁg;kñúg
TIRkugeT.
Tung Nget, MSc 7-25
26. 7-eFVIetsþsmμtikmμsRmab; p
⎧H o :p = p0 ⎧H o :p ≥ p0 ⎧H o :p ≤ p0
⎨ ⎨ ⎨
⎩H1 : p ≠ p 0 ⎩H1 : p < p0 ⎩H1 : p > p 0
bdiesd H ebI³ 0 bdiesd H ebI³
0 bdeisd H eb³
I0
Z > Zα 2 Z < − Zα Z > Zα
KMrUtagminGaRs½y KMrUtagGaRs½y ³smamaRtsaklsßiti
⎧p
⎪
⎪ p = XA ³smamaRtKMrUtag
⎪ s n
ps − p ps − p ⎪
⎪
Z= Z= Edl cMnYnFatEudlmanlkN³A
⎨X A : ç
p (1 − p ) N−n p (1 − p ) ⎪
× ³cMnYnéntémGegátkgKrMUtag
⎪n ø uñ
n N −1 n ⎪
⎪N³TMhsaklsßiti
M
⎪
⎩
Tung Nget, MSc 7-26
27. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
]TahrN_ ³ munnwge)aHeqñatKN³bkSmYy)anGHGagfaya:gtic 80% énRbCaBlrdæTaMgGs;
Edl)ancuHeQμaHe)aHeqñat[KN³bkSrbs;xøÜn. edIm,IepÞógpÞat;nUvkarGHGagenHeK)aneRCIserIs
KMrUsakécdnüEdlman 2000nak; nwgmanGñkKaMRTcMnYn 1550 nak;. edayeRbIRbU)abRcLM α = 0.05
etI karGHGagenHBitb¤eT?
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
H0: p ≥ 0.80
H1: p < 0.80
¬cMNaM³BaküKnøwH {ya:gehacNas;} ¦
CMhan 2³ RbU)abRcLM α = 0.05
CMhan 3³ sßitietsþ ( ) eRBaH np nig n(1-p) ≥ 5
Z=
ps − p
p 1− p
n
Tung Nget, MSc 7-27
28. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z < -Z α
α = 0.05 ⇒ p(Z < − z 0.05 ) = 0.05
⇔ p(−z 0.05 < Z < 0) = 0.4500
⇔ p(0 < Z < z 0.05 ) = 0.4500 ⇒ z 0.05 = 1.65
1550
− 0.80
ps − p
z= = 2000 = −2.80
p (1 − p ) 0.80 (1 − 0.80 )
n 2000
⇒ z = −2.80 < −1.65 Bt
i
CMhan 5³ seRmccitþnigbkRsaycemøIy³
dUecñHbdiesF H0 kñúgkMritkMhus 0>0% mann½yfaPsþútagRtg;cMNucenH
minKaMRTkarGHGagEdlfaGPi)alextþnwgRtLb;mkkan;dMENgecAhVay
extþ sRmab;ry³eBlbYnqñaMeToteT.
Tung Nget, MSc 7-28
29. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
]TahrN_ ³eKRtYtBinitüsþúkmanTMnijeRcIn EdlGñkTTYlxusRtUvGHGagfamanxUcya:gtic 3% .
eKeRCIsKMrUécdnüTMhM n=500 edayGegáteXIjTMnijxUc 14 ehIyedayyk α = 0 .05 .
etIGñkRtYtBinitüseRmccitþya:gNacMeBaHkarGHGagrbs;GñkTTYlxusRtUv .
k-krNIKMrUécdnüsamBaØminGaRs½y .
x-krNIKMrUécdnüsamBaØeRCIserIsmindak;eTAvij ebITMnijTaMgGs;; 3000 .
k-krNIKMrUécdnüsamBaØminGaRs½y
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
H0: p ≥ 0.03
H1: p < 0.03
¬cMNaM³BaküKnøwH {ya:gehacNas;} ¦
CMhan 2³ RbU)abRcLM α = 0.05p
p −
Tung Nget, MSc
CMhan 3³ sßitietsþ p(1− p) eRBaH np nig n(1-p) ≥ 5
Z= s
7-29
n
30. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z < -Z α
α = 0.05 ⇒ p(Z < − z 0.05 ) = 0.05 ⇔ p(− z 0.05 < Z < 0) = 0.4500
⇔ p(0 < Z < z 0.05 ) = 0.4500 ⇒ z 0.05 = 1.65
14
− 0.03
ps − p
z= = 500 = − 0.262
p (1 − p ) 0.0 3 × 0.97
n 500
⇒ z = − 0.2 6 2 mn tUc Cag
i − z 0.05 = − 1 . 65
CMhan 5³ seRmccitþnigbkRsaycemøIy³
dUecñH TTYlyk H0 )ann½yfakarGHGagrbs;GñkTTYlxusRtUvBit .
Tung Nget, MSc 7-30
32. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z < -Z α
α = 0.05 ⇒ p(Z < − z 0.05 ) = 0.025 ⇔ p(− z 0.05 < Z < 0) = 0.4500
⇔ p(0 < Z < z 0.05 ) = 0.4500 ⇒ z 0.05 = 1.65
14
− 0.03
ps − p 500
z= = = −0.2871
N−n p (1 − p ) 3000 − 500 0.03 × 0.97
× ×
N −1 n 3000 − 1 500
⇒ z = −0.2871 mntcCag − z
i U 0.05 = −1.65
CMhan 5³ seRmccitþnigbkRsaycemøIy³
dUecñH TTYlyk H0 )ann½yfakarGHGagrbs;GñkTTYlxusRtUvBit .
Tung Nget, MSc 7-32
33. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
]TahrN_ ³ shRKasmYy)anBinitüCaRbcaMnUvKuNPaBplitplrbs;xøÜn. qñaMknøgeTAplitplrbs;shRKas
)anxUc 5 % ehIyenAqñaMenHedIm,IRtYtBinitü eKeRCIserIs 400 plitpl CaKMrUécdnü edayeXIjmanxUc 28
plitpl . etIPaKryplitplxUcrbs;shRKasqñaMenHenAdEdl b¤eRcInCagqñaMmunedayyk α = 0.05.
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
⎧H0: p ≤ 0.05
⎨
⎩H1: p > 0.05
¬cMNaM³BaküKnøwH {eRcInCag} ¦
CMhan 2³ RbU)abRcLM α = 0.05
p −p
CMhan 3³ sßitietsþ Z= s
p (1 − p) eRBaH np nig n(1-p) ≥ 5
n
eKRtUveRbIKMrUécdnüminGaRs½y eRBaHfaminsÁal;TMhMrbs;saklsßiti
Tung Nget, MSc 7-33
34. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z > Z α
α = 0.05 ⇒ p(Z < −z0.05 ) = 0.025 ⇔ p(−z0.05 < Z < 0) = 0.4500
⇔ p(0 < Z < z0.05 ) = 0.4500 ⇒ z0.05 = 1.65
28
− 0.05
ps − p 400
z= = = 1.84
p (1 − p ) 0.05 (1 − 0.05 )
n 400
FCag z = 1.65
⇒ z = 1.84M 0.05
CMhan 5³ seRmccitþnigbkRsaycemøIy³
dUecñH bdiesF H0 )ann½yfaPaKryplitplxUcrbs;shRKasqñaMenH
eRcInCagqñaMmun .
Tung Nget, MSc 7-34
35. cb;edaybribUN_
GrKuNcMeBaHkarykcitþTukdak;¡
rrr<sss
Tung Nget, MSc 7-35
