Estimation and Confidence Intervals

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Estimation and Confidence Intervals

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 12. dMeNaHRsay ¬t¦ Tung Nget, MSc 6-12
  13. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 37. cb;edaybribUN_ GrKuNcMeBaHkarykcitþTukdak;¡ rrr<sss Tung Nget, MSc 6-37

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