CMBUkTI 7
             kareFVIetsþsmμtikmμelIKMrUtagmYy
                           ti elI
                     sßitiBaNiC¢...
kareFVIetsþsmμtikmμelIKMrUtagmYy
• vtßúbMNg³ enAeBlEdlGñkbBa©b;enAkñúgCMBUkenH GñknwgGac³
1. kMNt;niymn½yénsmμtikmμ nigkar...
kareFVIetsþsmμtikmμμelIKMrUtagmYy
  1-smμtikmμ nigkareFVIetsþsmμtikmμ
  2> dMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
  3-cMnu...
1-smμtikmμ nigkareFVIetsþsmμtikmμ
                          (Hypothesis and Hypothesis Testing)

smμtikmμCaBuMenalGMBItémø...
2> dMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
  CMhanTI1³ kMNt;smμtikmμsUnü (H ) nigsmμtikmμqøas; (H ) ³
                     ...
2> dMeNIkar 5 CMhansRmab;eFVIetsþsmμtikmμ
CMhanTI4³ begáItviFanénkarseRmccitþ.
témøvinicä½y³           CacMNucx½NÐrvagEdnE...
3-cMnucsMxan;edIm,IcgcaMBI                H0         nig   H1

• H0 : smμtikmμsUnü nig H : smμtikmμqøas;
                 ...
4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30

⎧H o :μ = μ 0        ⎧H o :μ ≥ μ 0       ⎧H o :μ ≤ μ 0
⎨                ...
4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
             ]TahrN_³ Rkumh‘un Jamestown Steel plitnigdMeLIgtu nigeRK...
4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
                                                  Z > Zα / 2
        ...
4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ KMrUsakmYyEdlmanTMhM 36 RtUveKeRCIserIsedayécdnüecjBIsakl s...
4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ Rkumhu‘nRsaebormYy)anGHGagfa cMNuHRsaeborCamFümkñúgmYykMbu:...
4-eFVIetsþsmμtikmμsRmab; μ krNIsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ KMrUsakmYyEdlmanTMhM 49 RtUveKeRCIserIsedayécdnüecjBIsaklsß...
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30
⎧H o :μ = μ 0             ⎧H o :μ ≤ μ 0            ⎧H o :μ ≥ μ 0
⎨    ...
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦
]TarhN_ ³ ma:suInqugkarehVsV½yRbvtþmYy RtUv)anGñklk;bBa¢a[qugmYyEB...
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦

    CMhan 4³ BaküriHKn;rbs;GñkTTYlTankarehVBit ¬bdiesF H0¦
    eb...
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦
]TahrN_ ³ Rkumhu‘nRsaebormYy)anGHGagfa cMNuHRsaeboCamFümkñúgmYy²kM...
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n ≥ 30 ¬t¦
  CMhan 4³ bdiesF H0 ebI          z > zα / 2
                   α
...
6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30
     enAeBlEdlKmøatKMrUsaklsßiti (σ) minsÁal; enaHKmøatKMrU (s)énKMrUt...
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
  ]TahrN_³
EpñkTamTarRkumh‘unFanara:b;rg McFarland raykarN_faéføcM...
5-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
           H0: μ ≥ $60
   ...
6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
]TahrN_ ³ rdækrTwkmanGagsþúkTwksMrab;pÁt;pÁg;TIRkugmYy EdleRbIR)as...
6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦
                                    x − μ0
     CMhan 3³ sßitietsþ...
6-eFVIetsþsmμtikmμsRmab; μ krNIminsÁl; σ nig n < 30 ¬t¦

x-krNIKMrUécdnüsamBaØeRCIsmindak;eTAvij ebIkñúgTIRkugenaHman
200 ...
CMhan 4³ karpÁt;pÁg;TwknwgxVH ¬bdiesF H0¦ ebI t > tα, n-1
bMENgEck Student dWeRkesrI n-1=15 tamtMélRbU)ab‘ÍlIet 0.05
eK)an...
7-eFVIetsþsmμtikmμsRmab; p
   ⎧H o :p = p0                 ⎧H o :p ≥ p0              ⎧H o :p ≤ p0
   ⎨                    ...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
]TahrN_ ³ munnwge)aHeqñatKN³bkSmYy)anGHGagfaya:gtic 80% énRbCaBlrdæTaMgGs;
  Edl)ancu...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z < -Z           α
   α = 0.05 ⇒ p(Z < − z 0.05 ) = 0.05
    ⇔...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
]TahrN_ ³eKRtYtBinitüsþúkmanTMnijeRcIn EdlGñkTTYlxusRtUvGHGagfamanxUcya:gtic 3% .
 eK...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z < -Z         α


   α = 0.05 ⇒ p(Z < − z 0.05 ) = 0.05 ⇔ p(−...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
x-krNIKMrUécdnüsamBaØGaRs½y
CMhan 1³ smμtikmμsUnü nig smμtikmμqøas;
          H0: p ≥...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z < -Z           α


   α = 0.05 ⇒ p(Z < − z 0.05 ) = 0.025 ⇔ ...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
]TahrN_ ³ shRKasmYy)anBinitüCaRbcaMnUvKuNPaBplitplrbs;xøÜn. qñaMknøgeTAplitplrbs;shRK...
7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦
CMhan 4³ bdiesF H0 ebI Z > Z        α

   α = 0.05 ⇒ p(Z < −z0.05 ) = 0.025 ⇔ p(−z0.0...
cb;edaybribUN_

          GrKuNcMeBaHkarykcitþTukdak;¡
                  rrr<sss

Tung Nget, MSc                          ...
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One-Sample Tests of Hypothesis

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One-Sample Tests of Hypothesis

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
  31. 31. 7-eFVIetsþsmμtikmμsRmab; p ¬]TahrN_¦ x-krNIKMrUécdnüsamBaØGaRs½y CMhan 1³ smμtikmμsUnü nig smμtikmμqøas; H0: p ≥ 0.03 H1: p < 0.03 ¬cMNaM³BaküKnøwH {ya:gehacNas;} ¦ CMhan 2³ RbU)abRcLM α = 0.05 p −p CMhan 3³ sßitietsþ N − n p(1− p) eRBaH np nig n(1-p) ≥ 5 Z= s × N −1 n Tung Nget, MSc 7-31
  32. 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. 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. 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. 35. cb;edaybribUN_ GrKuNcMeBaHkarykcitþTukdak;¡ rrr<sss Tung Nget, MSc 7-35

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