Post on 06-Apr-2018
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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NSSQKU\GIH I@NSSQKU\GIH I@
HI_KNBG\WHI_KNBG\W
Lr( N}nlaj Nsdnrg>>
S\N\GS\GCS NHNBWSGS
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Nssqku|gih i` Hirknbg|wNssqku|gih i` Hirknbg|w Knhw i` |ja s|n|gs|gcnb ka|jils |jn| ta tgbb nuubw ra~qgra
|ja nssqku|gih |jn| n pnrgnoba ir pnrgnobas nra hirknbbw
lgs|rgoq|al(
Tg|j kqb|gpnrgn|a s|n|gs|gcs" |ja nssqku|gih gs |jn| |ja
cikoghn|gih i` pnrgnobas `ibbits n kqb|gpnrgn|a hirknb
lgs|rgoq|gih(
Sghca |jara gs hi| n lgrac| |as| `ir kqb|gpnrgn|a hirknbg|w" ta
daharnbbw |as| ancj pnrgnoba ghlgpglqnbbw nhl nssqka |jn|
|jaw nra kqb|gpnrgn|a hirknb g` |jaw nra ghlgpglqnbbw hirknb"
|jiqdj |jgs gs hi| hacassnrgbw |ja cnsa(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Apnbqn|ghd Hirknbg|wApnbqn|ghd Hirknbg|w
\jara nra oi|j drnujgcnb nhl s|n|gs|gcnb ka|jils `ir apnbqn|ghd
hirknbg|w(
Drnujgcnb ka|jils ghcbqla |ja jgs|idrnk nhl hirknbg|w ubi|(
S|n|gs|gcnb ka|jils ghcbqla lgndhis|gc jwui|jasgs |as|s `ir
hirknbg|w" nhl n rqba i` |jqko |jn| snws n pnrgnoba gs
ransihnobw cbisa |i hirknb g` g|s sfathass nhl fqr|isgs jnpa
pnbqas oa|taah ¾>(5 nhl &>(5(
Hiha i` |ja ka|jils gs nosibq|abw la`ghg|gpa(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\rnhs`irkn|gihs\rnhs`irkn|gihs
Tjah n pnrgnoba gs hi| hirknbbw lgs|rgoq|al" ta cnh cran|a n|rnhs`irkal pnrgnoba nhl |as| g| `ir hirknbg|w( G` |ja|rnhs`irkal pnrgnoba gs hirknbbw lgs|rgoq|al" ta cnh
sqos|g|q|a g| gh iqr nhnbwsgs(
\jraa cikkih |rnhs`irkn|gihs nra= |ja bidnrg|jkgc|rnhs`irkn|gih" |ja s~qnra rii| |rnhs`irkn|gih" nhl |ja
ghparsa |rnhs`irkn|gih(
Nbb i` |jasa cjnhda |ja kansqrghd scnba ih |ja jirg}ih|nbnzgs i` n jgs|idrnk |i urilqca n |rnhs`irkal pnrgnoba |jn| gskn|jakn|gcnbbw a~qgpnbah| |i |ja irgdghnb pnrgnoba(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
http://slidepdf.com/reader/full/assumption-of-normality-dr-azadeh-asgari 5/27
Tjah \rnhs`irkn|gihs Li Hi|Tirf Tjah \rnhs`irkn|gihs Li Hi|Tirf
Tjah hiha i` |ja |rnhs`irkn|gihs ghlqcas hirknbg|w gh n
pnrgnoba" ghcbqlghd |jn| pnrgnoba gh |ja nhnbwsgs tgbb ralqca
iqr a``ac|gpahass n| glah|g`wghd s|n|gs|gcnb rabn|gihsjgus" g(a(ta bisa uitar(
Ta li jnpa |ja iu|gih i` cjnhdghd |ja tnw |ja gh`irkn|gih
gh |ja pnrgnoba gs raurasah|al" a(d( sqos|g|q|a saparnb
lgcji|ikiqs pnrgnobas `ir n sghdba ka|rgc pnrgnoba(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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UriobakUriobak >>
Gh |ja ln|nsa| DSS?555(snp" gs |ja `ibbitghd s|n|akah| |rqa"
`nbsa" ir nh ghcirrac| nuubgcn|gih i` n s|n|gs|gc9 Qsa 5(5> ns |ja
bapab i` sgdhg`gcnhca(
Onsal ih n lgndhis|gc jwui|jasgs |as| i` hirknbg|w" |i|nb jiqrs
suah| ih |ja Gh|arha| gs hirknbbw lgs|rgoq|al(
>(\
rqa?( \rqa tg|j cnq|gih
3( @nbsa
<( Ghcirrac| nuubgcn|gih i` n s|n|gs|gc
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Cikuq|ghd ³Azubira¼ Lascrgu|gpa S|n|gs|gcsCikuq|ghd ³Azubira¼ Lascrgu|gpa S|n|gs|gcs
\i cikuq|a |ja s|n|gs|gcs haalal
`ir apnbqn|ghd |ja hirknbg|w i` n
pnrgnoba" sabac| |ja Azubira¦
cikknhl `rik |ja Lascrgu|gpa
S|n|gs|gcs kahq(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Nllghd |ja Pnrgnoba |i oa Apnbqn|alNllghd |ja Pnrgnoba |i oa Apnbqn|al
@grs|" cbgcf ih |ja pnrgnoba
|i oa ghcbqlal gh |ja
nhnbwsgs |i jgdjbgdj| g|(
Sacihl" cbgcf ih rgdj|
nrrit oq||ih |i kipa |ja
jgdjbgdj|al pnrgnoba |i |ja
Lauahlah| Bgs| (
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Sabac|ghd S|n|gs|gcs |i oa Cikuq|alSabac|ghd S|n|gs|gcs |i oa Cikuq|al
\i sabac| |ja s|n|gs|gcs ̀ ir |jaiq|uq|" cbgcf ih |jaS|n|gs|gcs¦ cikknhl oq||ih(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Ghcbqlghd Lascrgu|gpa S|n|gs|gcsGhcbqlghd Lascrgu|gpa S|n|gs|gcs
@grs|" cbgcf ih |ja
Lascrgu|gpas cjacfoiz
|i sabac| g|( Cbanr |ja
i|jar cjacfoizas(
Sacihl" cbgcf ih |ja
Cih|ghqa oq||ih |i
cikuba|a |ja ra~qas|
`ir s|n|gs|gcs(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Sabac|ghd Cjnr|s @ir \ja Iq|uq|Sabac|ghd Cjnr|s @ir \ja Iq|uq|
\i sabac| |ja lgndhis|gc
cjnr|s `ir |ja iq|uq|"
cbgcf ih |ja Ub i|s¦
cikknhl oq||ih(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Ghcbqlghd Lgndhis|gc Ubi|s & S|n|gs|gcsGhcbqlghd Lgndhis|gc Ubi|s & S|n|gs|gcs
@grs|" cbgcf ih |ja H iha
iu|gih oq||ih ih |ja Oizubi|s
unhab sghca oizubi|s nra hi|
ns jabu`qb ns i|jar cjnr|s gh
nssassghd hirknbg|w(
Sacihl" cbgcf ih |ja H irknb g|w
ub i|s tg|j |as|s cjacfoiz |i
ghcbqla hirknbg|w ubi|s nhl |ja
jwui|jasgs |as|s `ir hirknbg|w(
\jgrl" cbgcf ih |ja J gs| id rnk
cjacfoiz |i ghcbqla n jgs|idrnk
gh |ja iq|uq|( Wiq knw tnh| |i
aznkgha |ja s|ak+nhl+ban` ubi| ns
tabb" |jiqdj G `ghl g| bass qsa`qb(
@ghnbbw" cbgcf ih |ja
Cih|ghqa oq||ih |i
cikuba|a |ja ra~qas|(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Cikuba|ghd |ja Suacg`gcn|gihs `ir |ja NhnbwsgCikuba|ghd |ja Suacg`gcn|gihs `ir |ja Nhnbwsgss
Cbgcf ih |ja IF oq||ih |i
cikuba|a |ja suacg g̀cn|gihs
`ir |ja nhnbwsgs nhl ra~qas|
SUSS |i urilqca |ja iq|uq|(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\ja Jgs|idrnk\ja Jgs|idrnk
\I\NB \GKA SUAH\ IH \JA GH\A_HA\
>55(5
75(5
:5(5
45(5
05(5
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5(5
Jgs|idrnk
@ r a ~ q a h c w
15
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35
?5
>5
5
S|l( Lap ; >1(31
Kanh ; >5(4
H ; 73(55
Nh ghg|gnb gkurassgih i` |ja
hirknbg|w i` |ja lgs|rgoq|gih cnh oa
dnghal ow aznkghghd |ja
jgs|idrnk(
Gh |jgs aznkuba" |ja jgs|idrnksjits n sqos|nh|gnb pgibn|gih i`
hirknbg|w cnqsal ow n az|rakabw
bnrda pnbqa gh |ja lgs|rgoq|gih(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\ja Hirknbg|w Ubi|\ja Hirknbg|w Ubi|
Hirknb ^+^ Ubi| i` \I\NB \GKA SUAH\ IH \JA GH\A_H
Iosarpal Pnbqa
>?5>55:505<5?55+?5+<5
A z u a c | a l H i r k
n b
3
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>
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\ja uriobak tg|j |ja hirknbg|w i` |jgs
pnrgnoba°s lgs|rgoq|gih gs ragh`ircal ow |ja
hirknbg|w ubi|(
G` |ja pnrgnoba tara hirknbbw lgs|rgoq|al" |ja
ral li|s tiqbl `g| |ja draah bgha parw cbisabw(
Gh |jgs cnsa" |ja ral uigh|s gh |ja quuar rgdj|
i` |ja cjnr| ghlgcn|a |ja sapara sfatghd
cnqsal ow |ja az|rakabw bnrda ln|n pnbqas(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\ja \as| i` Hirknbg|w\ja \as| i` Hirknbg|w
\as|s i` Hirknbg|w
(?<0 73 (555 (050 73 (555\I\NB \GKA SUAH\
( (
+n
+
a irs dh cnhca irrac ih(
Uriobak > nsfs noiq| |ja rasqb|s i` |ja |as| i` hirknbg|w( Sghca |ja snkuba sg}a gs bnrdar |jnh
15" ta qsa |ja Fibkidirip+Skgrhip |as|( G` |ja snkuba sg}a tara 15 ir bass" ta tiqbl qsa |ja
Sjnugri+Tgbf s|n|gs|gc ghs|anl(
\ja hqbb jwui|jasgs `ir |ja |as| i` hirknbg|w s|n|as |jn| |ja nc|qnb lgs|rgoq|gih i` |ja pnrgnoba gsa~qnb |i |ja azuac|al lgs|rgoq|gih" g(a(" |ja pnrgnoba gs hirknbbw lgs|rgoq|al( Sghca |ja urionogbg|w nssicgn|al tg|j |ja |as| i` hirknbg|w gs 2 5(55> gs bass |jnh ir a~qnb |i |ja bapab i` sgdhg g̀cnhca *5(5>'" ta ramac| |ja hqbb jwui|jasgs nhl cihcbqla |jn| |i|nb jiqrs suah| ih |jaGh|arha| gs hi| hirknbbw lgs|rgoq|al( *Hi|a= ta rauir| |ja urionogbg|w ns 25(55> ghs|anl i` (555|i oa cbanr |jn| |ja urionogbg|w gs hi| ranbbw }ari('
\ja nhstar |i uriobak > gs `nbsa(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\ja Nssqku|gih i` Hirknbg|w Scrgu|\ja Nssqku|gih i` Hirknbg|w Scrgu|
Nh SUSS scrgu| |i urilqca nbb i` |ja
iq|uq| |jn| ta jnpa urilqcal
knhqnbbw gs npngbnoba ih |ja ciqrsa
tao sg|a(
N |̀ar lithbinlghd |ja scrgu|" rqh g|
|i |as| |ja nssqku|gih i` bghanrg|w(Sabac| _qh Scrgu|¦
`rik |ja Q|gbg|gas kahq(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Sabac|ghd |ja Nssqku|gih i` Hirknbg|w Scrgu|Sabac|ghd |ja Nssqku|gih i` Hirknbg|w Scrgu|
@grs|" hnpgdn|a |i |ja `iblar
cih|nghghd wiqr scrgu|s nhl
jgdjbgdj| |ja
Hirknbg|wNssqku|gihNhl\r
nhs`irkn|gihs(SOS scrgu|(
Sacihl" cbgcf ih |ja _qh
oq||ih |i nc|gpn|a |ja scrgu|(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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Suacg`gcn|gihs `ir Hirknbg|w Scrgu|Suacg`gcn|gihs `ir Hirknbg|w Scrgu|
\ja la`nqb| iq|uq| gs |i li nbb i`
|ja |rnhs`irkn|gihs i` |ja pnrgnoba(
\i azcbqla sika |rnhs`irkn|gihs
`rik |ja cnbcqbn|gihs" cbanr |jacjacfoizas( \jgrl" cbgcf ih |jaIF
oq||ih |i rqh |ja scrgu|(
@grs|" kipa pnrgnobas
`rik |ja bgs| i` pnrgnobas
gh |ja ln|n sa| |i |ja
P nrgnob as | i \as| bgs| oiz(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\ja \as| i` Hirknbg|w\ja \as| i` Hirknbg|w
\as|s i` Hirknbg|w
(?<0 73 (555 (050 73 (555\I\NB \GKA SUAH\
( (
+n
+
a irs dh cnhca irrac ih(
\ja scrgu| urilqcas |ja snka
iq|uq| |jn| ta cikuq|al knhqnbbw"gh |jgs aznkuba" |ja |as|s i`
hirknbg|w(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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UriobakUriobak ??
Gh |ja ln|nsa| DSS?555(snp" gs |ja `ibbitghd s|n|akah| |rqa"
`nbsa" ir nh ghcirrac| nuubgcn|gih i` n s|n|gs|gc9
Onsal ih |ja rqba i` |jqko `ir |ja nbbitnoba kndhg|qla i`
sfathass nhl fqr|isgs" |i|nb jiqrs suah| ih |ja Gh|arha| gs
hirknbbw lgs|rgoq|al(
>( \rqa
?( \rqa tg|j cnq|gih
3( @nbsa
<( Ghcirrac| nuubgcn|gih i` n s|n|gs|gc
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\noba i` Lascrgu|gpa S|n|gs|gcs\noba i` Lascrgu|gpa S|n|gs|gcs
Lascrgu|gpas
( (
(
>3(:73
(
(
(
(
(
(
((
( (
( (
anh
itar iqh
Quuar Oiqhl
71! Cih`glahca
Gh|arpnb `ir Kanh
r kka anh
a nh
nr nhca
( ap n ih
h kqk
nz kqk
nhdah ar~qnr a nhda
athass
qr is s
\I\NB \GKA SUAH\
IH \JA GH\A_HA\
(
\i nhstar uriobak ?"
ta biif n| |ja pnbqas
`ir sfathass nhlfqr|isgs gh |ja
Lascrgu|gpas |noba(
\i` |jqko crg|argn i` >(5( \ja pnrgnoba gs hi| hirknbbw
lgs|rgoq|al(
ja sfathass nhl fqr|isgs `ir |ja pnrgnoba oi|j azcaal |ja rqba
\ja nhstar |i uriobak ? g` `nbsa(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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UriobakUriobak 33Gh |ja ln|nsa| DSS?555(snp" gs |ja `ibbitghd s|n|akah| |rqa"
`nbsa" ir nh ghcirrac| nuubgcn|gih i` n s|n|gs|gc9 Qsa 5(5> ns |ja
bapab i` sgdhg`gcnhca(
Onsal ih n lgndhis|gc jwui|jasgs |as| i` hirknbg|w" /|i|nb jiqrs
suah| ih |ja Gh|arha|/ gs hi| hirknbbw lgs|rgoq|al( N bidnrg|jkgc
|rnhs`irkn|gih i` /|i|nb jiqrs suah| ih |ja Gh|arha|/ rasqb|s gh n
pnrgnoba |jn| gs hirknbbw lgs|rgoq|al(
>( \rqa
?( \rqa tg|j cnq|gih
3( @nbsa
<( Ghcirrac| nuubgcn|gih i` n s|n|gs|gc
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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\ja \as| i` Hirknbg|w\ja \as| i` Hirknbg|w
\as|s i` Hirknbg|w
(5<4 73 (?55- (77< 73 (71>
(>>: 73 (553 (:0: 73 (555
(?:: 73 (555 (<71 73 (555
Bidnrg|jk i` HA\GKA
S~qnra _ii| i` HA\GKA
Ghparsa i` HA\GKA
( (
+n
+
s s n itar iqh i | a |rqa s dh cnhca((
a irs dh cnhca irrac ih(
Uriobak 3 suacg`gcnbbw nsfs noiq| |ja rasqb|s i` |ja |as| i` hirknbg|w `ir |ja
bidnrg|jkgc |rnhs`irkn|gih( Sghca iqr snkuba sg}a gs bnrdar |jnh 15" ta qsa |ja
Fibkidirip+Skgrhip |as|(
\ja hqbb jwui|jasgs `ir |ja Fibkidirip+Skgrhip |as| i` hirknbg|w s|n|as |jn| |janc|qnb lgs|rgoq|gih i` |ja |rnhs`irkal pnrgnoba gs a~qnb |i |ja azuac|al lgs|rgoq|gih"g(a(" |ja |rnhs`irkal pnrgnoba gs hirknbbw lgs|rgoq|al( Sghca |ja urionogbg|wnssicgn|al tg|j |ja |as| i` hirknbg|w *5(?55' gs dran|ar |jnh |ja bapab i` sgdhg`gcnhca"ta `ngb |i ramac| |ja hqbb jwui|jasgs nhl cihcbqla |jn| |ja bidnrg|jkgc |rnhs`irkn|gihi` |i|nb jiqrs suah| ih |ja Gh|arha| gs hirknbbw lgs|rgoq|al(
\ja nhstar |i uriobak 3 gs |rqa(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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I|jar Uriobaks ih Nssqku|gih i` Hirknbg|wI|jar Uriobaks ih Nssqku|gih i` Hirknbg|w N uriobak knw nsf noiq| |ja nssqku|gih i` hirknbg|w `ir n
hikghnb bapab pnrgnoba( \ja nhstar tgbb oa ³Nh ghnuuriurgn|anuubgcn|gih i` n s|n|gs|gc¼ sghca |jara gs hi azuac|n|gih |jn| n
hikghnb pnrgnoba oa hirknb(
N uriobak knw nsf noiq| |ja nssqku|gih i` hirknbg|w `ir nhirlghnb bapab pnrgnoba( G` |ja pnrgnoba ir |rnhs`irkal pnrgnoba gshirknb" |ja cirrac| nhstar |i |ja ~qas|gih gs ³\rqa tg|j
cnq|gih¼ sghca ta knw oa ra~qgral |i la`ahl |ran|ghd nh irlghnbpnrgnoba ns ka|rgc(
^qas|gihs tgbb suacg`w n bapab i` sgdhg`gcnhca |i qsa nhl |jas|n|gs|gcnb apglahca quih tjgcj wiq sjiqbl onsa wiqr nhstar(
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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S|aus gh Nhstarghd ^qas|gihs noiq| |jaS|aus gh Nhstarghd ^qas|gihs noiq| |ja
Nssqku|gih i` Hirknbg|wNssqku|gih i` Hirknbg|w ¾ ¾ ^qas|gih^qas|gih >>\ja `ibbitghd gs n dqgla |i |ja lacgsgih uricass `ir nhstarghd
uriobaks noiq| |ja hirknbg|w i` n pnrgnoba=
Lias |ja s|n|gs|gcnb
apglahca squuir|
hirknbg|w nssqku|gih9
Was
Hi
Ghcirrac|nuubgcn|gih i` n
s|n|gs|gc
Was
HiGs |ja pnrgnoba |i oa
apnbqn|al ka|rgc9
@nbsa
Nra nhw i` |ja ka|rgc
pnrgnobas irlghnb bapab9
Was
\rqaHi
\rqa Tg|j Cnq|gih
8/3/2019 Assumption of Normality * Dr. Azadeh Asgari
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S|aus gh Nhstarghd ^qas|gihs noiq| |jaS|aus gh Nhstarghd ^qas|gihs noiq| |ja
Nssqku|gih i` Hirknbg|wNssqku|gih i` Hirknbg|w ¾ ¾ ^qas|gih^qas|gih ??
\ja `ibbitghd gs n dqgla |i |ja lacgsgih uricass `ir nhstarghd
uriobaks noiq| |ja hirknbg|w i` n |rnhs`irkn|gih=
S|n|gs|gcnb apglahca
squuir|s hirknbg|w9
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