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
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. 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. 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. 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. 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
