Two-Sample Tests of Hypothesis

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Two-Sample Tests of Hypothesis

  1. 1. CMBUkTI 8 kareFVIetsþsmμtikmμelIKMrUtagBIr 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 8-1
  2. 2. kareFVIetsþsmμtikmμelIKMrUtagBIr • vtßúbMNg³ enAeBlEdlGñkbBa©b;enAkñúgCMBUkenH GñknwgGac³ 1. eFVIetsþsmμtikmμsþIGMBIPaBxusKñarvagmFümsaklsßitiÉkraCBIr 2. eFVIetsþsmμtikmμsþIGMBIPaBxusKñarvagsmamaRtsaklsßitiBIr 3. eFVIetsþsmμtikmμsþIGMBIPaBxusKñaCamFümrvagtémøGegátKU b¤GaRsy½ 4. yl;BIPaBxusKñarvagKMrUtagGaRsy½nigKMrUtagminGaRsy½ Tung Nget, MSc 8-2
  3. 3. eFVIkareRbobeFobsaklsßitiBIr-]TahrN_ 1. etImanPaBxusKñakñúgtémømFüménGclnRTBükñúgRsukEdl)anTijeday Pñak;garePTRbul nigPñak;garePTRsIenAkñúgTIRkugPñMeBjEdrrWeT? 2. etImanPaBxusKñakñúgcMnYnmFüménplitplxUcEdlRtUv)anplit enAevnéf¶ nigenAevnresolenAeragcRk Kimble Products EdrrWeT? 3. etImanPaBxusKñakñúgcMnYnmFüméné;f¶Gvtþmanrvagkmμkrekμg¬GayuticCag 21qñaM¦ nigkmμkrvy½cMNas;¬GayueRcInCag 60qñaM¦ enAkñúg]sSahkmμ Gaharrhs½EdrrWeT? 4. etImanPaBxusKñakñúgsmamaRténnisSiteroncb;enAsaklviTüaly½rdæ nignisSiteroncb;enAsaklviTüaly½ÉkCnEdlRblgCab;cUlkñúgRkbxNн rdæenAelIkdMbUgEdrrWeT? 5. etImankarekIneLIgkñúgGRtaplitEdrrWeTRbsinebIeKcak;tRnþIenAkénøgplit? Tung Nget, MSc 8-3
  4. 4. 1-eRbobeFobmFümsaklsßitiBIr (Comparing Two Population Means) (n ≥ 30 ) • minmankarsnμt;sþIGMBIragénsaklsßiti • KMrUtagKW)anBIsaklsßitiminGaRs½ycMnYn2 etsþsgxag etsþxagtUc etsþxagFM ⎧ H o : μ1 = μ 2 ⎧ H o : μ1 ≥ μ 2 ⎧ H o : μ1 ≤ μ 2 ⎨ ⎨ ⎨ ⎩ H 1 : μ1 ≠ μ 2 ⎩ H 1 : μ1 < μ 2 ⎩ H 1 : μ1 > μ 2 bdie sd H ebI³ 0 bdei s d H ebI³ 0 bdiesd ebI³ H0 Z > Zα 2 Z < −Zα Z > Zα rUbmnþsRmab;karKNna sßitietsþ³ e bWI sÁa l ; σ nig σ 1 2 eb I m n s aÁ l ; σ ng σ i 1 i 2 X1 − X 2 X1 − X 2 z= z= σ1 2 σ2 2 s1 s2 + 2 + 2 n1 n2 n1 n 2 Tung Nget, MSc 8-4
  5. 5. 1-eRbobeFobmFümsaklsßitiBIr (Comparing Two Population Means) ]TahrN_³ meFüa)aygayRsYleQμaH U-Scan RtUv)aneKdak;[eRbIR)as;enA ÉTItaMg Byrne Road Food-Town. GñkRKb;RKghagcg;dwgfaetIry³eBlKitluyCamFüm edayeRbIR)as;viFIsaRsþKitluyKMrUFmμta eRbIeBlyUrCagkareRbI U-Scan EdlrWeT. nag)anRbmUlB½t’manKMrUtadUcxageRkam. ry³eBlRtUv)anvas;Kitcab;BIGtifiCncUl kñúgCYrrhUtdl;fg;rbs;BUkeKdak;kñúgreTH. dUecñHry³eBlrYmbeBa©ÚlTaMgry³eBlrgcaM kñúgCYrnigry³eBlKitluy. Tung Nget, MSc 8-5
  6. 6. dMeNaHRsay-¬eRbobeFobmFümsaklsßitiBIr¦ CMhan 1 kMNt;smμtikmμsUnü (H ) nigsmμtikmμqøas; (H ) 0 1 CMhan 4 begáItviFanénkarseRmccitþ³ (kMNt;sMKal;³ BaküKnøwH {ry³eBlyUrCag}) bdiesF H RbsinebI Z > Zα 0 Z > 2.33 H0: µS ≤ µU H1: µS > µU CMhanTI 5 kMNt;témø Z nigeFVIkarseRmccitþ³ CMhan 2 eRCIserIsRbU)abkMhus z= Xs − Xu = 5.5 − 5.3 = 0.2 = 3.13 σs σ u 0.064 α = 0.01 dUcmankñúglMhat; 2 2 0.40 2 0.30 2 + + ns nu 50 100 CMhan 3 kMNt;sßitietsþ eRbIbMENgEck Z-distribution eRBaHsÁal; σ Xs − Xu z= σs σu 2 2 + ns n u karseRmccitþKWRtUvbdiesFsmμtikmμsUnü. dUecñHviFIsaRsþ U-Scan KWrhs½Cag. Tung Nget, MSc 8-6
  7. 7. etsþKMrUtagBIrsþIGMBI smamaRt eyIgGegátemIlfaetIKMrUtagBIrRsg;ecjBIsaklsßitiBIrEdlmansmamaRtesμIKñaEdrrWeT. etsþsgxag etsþxagtUc etsþxagFM ⎧ H o :p1 = p 2 ⎧ H o : p1 ≥ p 2 ⎧ H o : p1 ≤ p 2 ⎨ ⎨ ⎨ ⎩ H1 :p1 ≠ p 2 ⎩ H 1 : p1 < p 2 ⎩ H 1 : p1 > p 2 bdie sd H ebI³ 0 bdei s d H ebI³ 0 bdiesd ebI³H0 Z > Zα 2 Z < −Zα Z > Zα rUbmnþsRmab;karKNna sßitietsþ³ ⎪ ³cMnYn{eCaKC½y}kñgKrMUtagTI1 ⎧ x1 u p s1 − p s 2 ³cnn{eCaKC½y}kgKMrUtagTI1 ⎪ x2 ⎪ MY ñu z= Edl ³cMnnéntémøGegátkñugKrMtagTI1 Y U ⎪ n1 ⎪ p c (1 − p c ) p c (1 − p c ) ⎨ + ³cMnnéntémGegtkgKrMUtagTI1 ⎪n 2 Y ø á uñ n1 n2 ⎪ x1 + x 2 ³smamaRtén{eCaKCy}kgKMrUtagTI1 ⎪ p s1 ½ ñu smamaRtrm³ Y pc = ⎪ n1 + n 2 ³smamaRtén{eCaKCy}kñugKrMUtagT2 ⎪ps 2 ⎩ ½ I Tung Nget, MSc 8-7
  8. 8. etsþKMrUtagBIrsþIGMBI smamaRt Rkumh‘un Manelli Perfume fμI²enH)anbegáItxøinRkGUbfμI. Rkumh‘unmanKeRmaglk;elITIpSar eday dak;eQμaH Heavenly. karsikSaBITIpSarCaeRcIn)ancg¥úlbgðajfa Heavenly manskþanuBlPaB TIpSarya:gl¥. Epñklk;enAÉ Manelli cab;GarmμN_ faetImanPaBxusKñakñúgsmamaRténRsþIvy½ekμg nigvy½cas; EdlnwgTij Heavenly RbsinebIvaRtUdak;lk;elITIpSar. KMrUtagRtUveKRbmUlBIRkummin GaRsy½Kña. RsþIEdlRtUveKeFVIKMrUtagRtUveKsYrfaetInagcUlcitþkøinRkGUbya:gxøaMgrhUtTijmYydbEdrrWeT. CMhan 1³ smμtikmμsUnü nig smμtikmμqøas; ¬BaküKnøwH {manPaBxusKña}¦ H0: p1 = p2 H1: p1 ≠ p2 CMhan 2³ RbU)abRcLM α = 0.05 p s1 − p s 2 CMhan 3³ sßitietsþ z= p c (1 − p c ) p c (1 − p c ) + n1 n2 Tung Nget, MSc 8-8
  9. 9. etsþKMrUtagBIrsþIGMBI smamaRt CMhan 4³ bdiesF H 0 ebI b¤ Z < - Z Z > Zα/2 α/2 Z > 1.96 b¤ Z < -1.96 tag ps1 = smamaRtRsþIekμg p = smamaRtRsþIcas; s2 x1 19 x2 62 ps1 = = = 0.19 ps2 = = = 0.31 n1 100 n 2 200 x1 + x 2 19 + 62 81 pc = = = = 0.27 n1 + n 2 100 + 200 300 ps1 − ps2 0.19 − 0.31 z= = = −2.21 pc (1 − pc ) pc (1 − pc ) 0.27 (1 − 0.27 ) 0.27 (1 − 0.27 ) + + n1 n2 100 200 CMhan 5³ seRmccitþnigbkRsaycemøIy³ Z=-2.21 sßitkñúgtMbn;e)aHbg;ecal. dUecñH bdiesF H0 Rtg;RbU)abRclM 0.05. Tung Nget, MSc 8-9
  10. 10. eRbobeFobmFümsaklsßitiedayminsÁal;KmøatKMrU ¬etsþ t rYm¦ bMENgEck t RtUveRbICa sßitietsþRbsinebIKMrUtag1 b¤eRcInCagmYyénKMrUtag mancMnYntémøGegát < 30. eyIgRtUvsnμt;dUcteTA³ 1- saklsßitiTaMgBIrRtUvEteKarBtamc,ab;nr½mal;. 2- saklsßitiRtUvEtmanKmøatKMrUesμIKña. 3- KMrUtagRtUvTajecjBIsaklsßitiminGaRsy½Kña. karEsVgrktémøénsßitietsþRtUvkar 2 CMhan³ 1- pþúMKmøatKMrUKMrUtag 2 s = ( n − 1) s + ( n − 1) s 1 2 1 2 2 2 n +n −2 p 2- eRbIKmøatKMrUpþúM kñúgrUbmnþ 1 2 x −x t= 1 2 ⎛ 1 1 ⎞ s2 ⎜ p + ⎟ ⎝ n1 n 2 ⎠ Tung Nget, MSc 8-10
  11. 11. 1-eRbobeFobmFümsaklsßitiBIr (Comparing Two Population Means) (n < 30 ) etsþsgxag etsþxagtUc etsþxagFM ⎧ H o : μ1 = μ 2 ⎧ H o : μ1 ≥ μ 2 ⎧ H o : μ1 ≤ μ 2 ⎨ ⎨ ⎨ ⎩ H 1 : μ1 ≠ μ 2 ⎩ H 1 : μ1 < μ 2 ⎩ H 1 : μ1 > μ 2 bdie sd H ebI³ 0 bdei s d H ebI³ 0 bdiesd ebI³ H0 t > tα 2 t < − tα t > tα x1 − x 2 rUbmnþsRmab;karKNna sßitietsþ³ t= ⎛ 1 1 ⎞ s2 ⎜ p + ⎟ ⎝ n1 n 2 ⎠ s 2 = ( n1 − 1) s12 + ( n 2 − 1) s 2 2 n1 + n 2 − 2 p Tung Nget, MSc 8-11
  12. 12. eRbobeFobmFümsaklsßitiedayminsÁal;KmøatKMrU ¬etsþ t rYm¦-]TahrN_ ]TahrN_³ Rkumh‘un plitnigpÁúMma:sIunkat;esμAEdlRtUv)andwkCBa¢ÚneTAGñklk;TUTaMgshrdæGaemrik nigkaNada. nitiviFIxusKñaBIrya:gRtUv)aneKesñIsRmab;temøIgma:sIunelIeRKag énma:sIunkat;esμA. sMnYr ³ etImanPaBxusKñakñúgry³eBlCamFümedIm,ItemøIgma:sIunelIeRKagénma:sIunkat;esμAEdrrWeT? edIm,IvaytémøviFIsaRsþTaMgBIr eKseRmccitþeFVIkarsikSaBIry³eBlnigclna. KMrUtagénkmμkr 5nak;RtUv)anvas;eBledayeRbIR)as;viFIsaRsþ Welles nig 6nak;edayeRbIR)as;viFIsaRsþ Atkins. plénkarBiesaFCanaTImandUcxageRkam³ etImanPaBxusKñakñúgry³eBltemøICamFüm edayeRbIRbU)abRcLM 0.10? Tung Nget, MSc 8-12
  13. 13. eRbobeFobmFümsaklsßiti-minsÁal;KmøatKMrU ¬etsþ t rYm¦-]TahrN_ CMhan 1 kMNt;smμtikmμsUnü (H ) nigsmμtikmμqøas; (H ) 0 1 ( BaküKnøwH {etImanPaBxusKñarWeT?}) H0: µ1 = µ2 H1: µ1 ≠ µ2 CMhan 2 eRCIserIsRbU)abkMhus α = 0.10 CMhanTI 5 kMNt;témø Z nigeFVIkarseRmccitþ³ ( n1 −1) s12 + ( n2 −1) s2 = ( 5 −1)( 2.9155) + ( 6 −1)( 2.0976) 2 2 2 2 s = = 6.2222 n1 + n2 − 2 5+ 6−2 p CMhan 3 kMNt;sßitietsþ eRbIbMENgEck x1 − x2 4−5 t-test eRBaHminsÁal;KmøatKMrUTaMgBIr t = = = − 0 .6 6 2 ⎛ 1 1 ⎞ ⎛1 1⎞ 6 .2 2 2 2 ⎜ + ⎟ b:uEnþsnμt;faesμIKña. s2 ⎜ p ⎝ n1 + ⎟ n2 ⎠ ⎝5 6⎠ CMhan 4 begáItviFanénkarseRmccitþ³ bdiesF H RbsinebI³ 0 t > tα/2, n1+n2-2 b¤ t < - tα/2, n +n -2 1 2 -0.662 t > t.05,9 b¤ t < - t.05,9 eyIgsnñidæanfaminmanPaBxusKñakñúgry³eBlCamFümkñúg t > 1.833 b¤ t < - 1.833 kartemøIgma:sIunelIeRKagedayeRbIR)as;viFIsaRsþTaMgBIr. Tung Nget, MSc 8-13
  14. 14. eRbobeFobmFümsaklsßitieBlEdlKmøatKMrUsaklsßitiminesμIKña ( σ 2 1 ≠ σ2 2 ) RbsinebIvaminsmehtuplkñúgkarsnμt;;faKmøaøatKMrUsaklsßitiminesμIμKña eyIgebI sßiti t. KmøatKMrUKMrUtag nwg lkñgkarsnμt aKm tKM aklsß es karsn sß t. KmøatKM [saKlsß RtUveRbICMnYs[saKlsßiti. xageRkam³ dWeRkesrIRtUvEktRmUvdUcxageRkam³ etsþsgxag etsþxagtUc etsþxagFM ⎧ H o : μ1 = μ 2 ⎧ H o : μ1 ≥ μ 2 ⎧ H o : μ1 ≤ μ 2 ⎨ ⎨ ⎨ ⎩ H 1 : μ1 ≠ μ 2 ⎩ H 1 : μ1 < μ 2 ⎩ H 1 : μ1 > μ 2 bdie sd H ebI³ 0 bdei s d H ebI³ 0 bdiesd ebI³ H0 t > tα 2 t < − tα t > tα rUbmnþsRmab;karKNna sßitietsþ³ Tung Nget, MSc 8-14
  15. 15. eRbobeFobmFümsaklsßitiedaymanKmøatKMrUsaklsßitiminesμIKña ]TahrN_³ buKÁlikenAkññúgTIBiesaFn_etsþBIGñkTij kMBugEtvaytémøBIkarRsUbcUlrbs;kEnSgRkdas;. li enAkgTI kTi EtvaytémøBI BUkeKcg;eRbobeFobQuténkEnSg store brand CamYyQutRsedogKññaénkEnSg name brand . énkEnSg RsedogK énkEnSg cMeBaHma:knImYy BYkeK)anRClk;bnÞHénRkdascUlkñúgGagénvtßúrav ykmkbgðÚrrTwkdak;kñúgFugkñúgry³eBl Gag énRkdascU kñgGagénvtßrav Tw gFu kñgry³eBl ry 2naTIdUcKñañ bnÞab;mkvas;brimaNénvtßúrßravEdlRkdasmanBIkñúgFug. KMrUtagécdnüénkEnSgRkdas store K aNénvt avEdlRkdasmanBI gFu agécdnüénkEnSgRkdas brand cMnYn9kEnSg name brand )anRsUbbrimaNvtßravCamIlIlItdUcxageRkam³ aNvtßúravCamI xageRkam³ 8 8 3 1 9 7 5 5 12 KMrUtagécdnüminGaRsy½énkEnSg cMnYn12kEnSg)anRsUbbrimaNvtßúrßravCamIlIlItdUcxageRkam³ agécdnümi GaRsy½ aNvt avCamI xageRkam³ 12 11 10 6 8 9 9 10 11 9 8 10 cUreRbIRbU)abRcLM 0.10 ehIycUreFVIetsþfaetImanPaBxusKñakñúñgbrimaNCamFüménvtßúrßravEdlRsUbeday manPaBxu Kñ kgbri aNCamFüménvt avEdlRsU kEnSgTaMgBIrRbePTEdrrWeT. lT§plEdlpþl;eday SPSS bgðajfa³ jfa³ Tung Nget, MSc 8-15
  16. 16. eRbobeFobmFümsaklsßitiedaymanKmøatKMrUsaklsßitiminesμIKña dMeNaHRsay CMhan 1 kMNt;smμtikmμsUnü (H ) nigsmμtikmμqøas; (H ) 0 1 ( BaküKnøwH {etImanPaBxusKña>>>>>rWeT?}) H0: µ1 = µ2 H1: µ1 ≠ µ2 CMhan 2 eRCIserIsRbU)abkMhus α = 0.10 CMhan 3 kMNt;sßitietsþ eyIgeRbIbMENgEck t-test krNIva:rü:g;minesμIKña CMhanTI 5 kMNt;témø t nigeFVIkarseRmccitþ³ CMhan 4 begáItviFanénkarseRmccitþ³ bdiesF H RbsinebI³ 0 t > tα/2d.f. b¤ t < - tα/2,d.f. eday t = -2.478 < -1.812 t > t0.05,10 b¤ t < - t0.05, 10 dUecñHeyIgRtUvsbdiesFsmμtikmμsUnü. eyIgsnñidæanfa t > 1.812 b¤ t < -1.812 GRtaRsUbTwkCamFümsRmab;kEnSTaMg2KWminesμIKμaeT. Tung Nget, MSc 8-16
  17. 17. 5-kareRbobmFümsaklsßitiGaRs½yKñaBIr etsþsgxag etsþxagtUc etsþxagFM ³deWRkesrI ⎧n − 1 ⎪ ⎧H o :μd = 0 ⎧H o :μ d ≥ 0 ⎧H o :μ d ≤ 0 Edl ⎪³mFüménPaBxsKña ⎪d u ⎨ ⎨ ⎨ ⎨ ³KMlaKrMUénPaBxsKña u ⎩ H1 : μ d ≠ 0 ⎩ H1 :μ d < 0 ⎩ H1 :μ d > 0 ⎪s d ⎪ d ³cMnYnénKU¬PaBxsKña ¦ ⎪n ⎩ u krNI n ≥ 30 sßitietsþ³ => Z= σd / n ]TahrN_³ bdie sd H ebI³ bdeisd H ebI³ 0 0 bdiesd H ebI³ 0 - RbsinebIGñkcg;TijLanGñknwg Z > Zα 2 Z < − Zα Z > Zα RkeLkemIlLanRbePTdUcKμaenA kEnøgQμÜjBIrrWeRcInkEnøgehIyeRbob krNI n < 30 => sßitietsþ³ sß t= d eFobtémørbs;va. sd / n - RbsinebIGñkcg;vas;BIRbsiTiPaBén bdie sd H ebI³ bdeisd H ebI³ bdiesd H ebI³ rbbGahar GñknwgføwgGñktmGahar t > tα 0 t < −tα 0 t > tα 0 enAeBlcab;epþImnigenAeBlbBa©b;én 2 kmμviFI. KMrUtagGaRsy½KWCaKMrUtagEdlRtUveKpÁÚ b¤ Tak;Tgnwgm:UdNamYy. Tung Nget, MSc 8-17
  18. 18. 5-kareRbobmFümsaklsßitiGaRs½yKñaBIr ]TahrN_³ Rkumh‘unh‘Nickel Savings and Loan h‘ cg;eRbobeFobRkumh‘unBIrEdlRtUveRbI edIm,IvaytémøpÞH nigkMNt;eBlsRmab;karvaytémø. lT§pl EdlraykarN_ aytémøpÞ arvaytémø CaBan;duløa RtUvbgðajkñúgtaragxageRkam. Rtg;kMritRbU)abRcLM 0>05 jkñgtaragxageRkam. etIeyIgGacsnññidæanfa vamanPaBxusKñakñúgtémøCamFüménpÞHTaMgenHEdrrWeT? Gacsn anfa vamanPaBxu Kñ kñgtémøCamFüménpÞ t amF Tung Nget, MSc 8-18
  19. 19. 5-kareRbobmFümsaklsßitiGaRs½yKñaBIr CMhan 1 kMNt;smμtikmμsUnü (H ) nigsmμtikmμqøas; (H ) 0 1 H0: µd = 0 l T§ pl H1: µd ≠ 0 CMhan 2 eRCIserIsRbU)abkMhus α = 0.05 CMhan 3 kMNt;sßitietsþ CMhanTI 5 kMNt;témø t nigeFVIkarseRmccitþ³ eyIgeRbIbMENgEck t-test krNIva:rü:g;minesμIKña CMhan 4 begáItviFanénkarseRmccitþ³ bdiesF H RbsinebI³ 0 eday t = 3.305 > 2.262dUecñHeyIgRtUvsbdiesF H . 0 t > tα/2, n-1. b¤ t < - tα/2, n-1 eyIgsnñidæanfa vamanPaBxusKñakñúgtémøCamFüménpÞH t > t0.025, 9 b¤ t < - t0.025, 9 EdlRtUvvaytémøTaMgenH. t > 2.262 b¤ t < -2.262 Tung Nget, MSc 8-19
  20. 20. cb;edaybribUN_ GrKuNcMeBaHkarykcitþTukdak;¡ rrr<sss Tung Nget, MSc 8-20

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