Tsu-2011 - ieeetsu

(sadac z
aris N(0,1)
-is zeda -kritikuli wertili anu kritikuli mni-
Svneloba C.V.).
1 ( z), Tu H1 : a1 a2
0;
P - mniSvneloba: P ( z), Tu H1 : a1 a2
0;
2 [1 (| z |)], Tu H1 : a1 a2
0.
gadawyvetileba: Tu z C.R., maSin H 0
hipoTezas ukuvagdebT, winaaRmdeg
SemTxvevaSi amis safuZveli ara gvaqvs.
P - mniSvnelobis meTodi: Tu P , maSin H
0
hipoTezas ukuvagdebT
mniSvnelovnebis doniT, winaaRmdeg SemTxvevaSi amis safuZveli ara
gvaqvs.
(1 )
saimedoobis ndobis intervali saSualoTa sxvaobisaTvis:
'2 '2 '2 '2
( xn ym) z/2 s1 / ns2 / m a1 a2 ( xn ym) z/2 s1 / n s2
/ m .
SeniSvna: im SemTxvevaSic, roca Cven vamowmebT hipoTezas imis Sesaxeb,
rom saSualoTa Soris gansxvaveba aris ara nuli, aramed raime konkretuli
ricxvi ( a 1
a 2
c ), kriteriumis statistikad isev ganixileba statistika:
( X ) (
1 2)
as
nY m a a
Z
N(0,1)
.
S / n S / m
'2 '2
1 2
magaliTebis amoxsnis nimuSebi:
magaliTi 1. saerTaSoriso statistikuri asociaciis monacemebiT
londonSi sastumros oTaxis saSualo Rirebuleba aris $88.42, xolo parizSi
ki $80.61. davuSvaT, rom TiToeul SemTxvevaSi aRebulia 50 sxvadasxva
sastumros monacemi da Sesworebuli SerCeviTi standartuli gadaxrebia
Sesabamisad $5.62 da $4.83. 0.05 mniSvnelovnebis doniT aris Tu ara
arsebiTi gansxvaveba saSualoebs Soris? aageT 95%-iani ndobis intervali
saSualoTa sxvaobisaTvis.
amoxsna. CamovayaliboT ZiriTadi da alternatiuli hipoTezebi:
H0 : a1 a2
0, H 1
: a 1
a
2
0. vipovoT kritikuli mniSvnelobebi:
CV . . z
/2
z0.025
1.96 .
gamovTvaloT kriteriumis mniSvneloba:
( xn
ym) ( a1 a2) (88.42 80.61) 0
z 7.45 .
'2 '2 2 2
s1 / n s2
/ m 5.62 /50 4.83 /50
vinaidan, 7.45 > 1.96, amitom nulovani hipoTeza unda ukuvagdoT, anu
saSualoebs Soris gansxvaveba arsebiTia.
avagoT ndobis intervali. am SemTxvevaSi 95% (1 ) 100% , saidanac
0.025 . Sesabamisad, z /2. amitom ndobis intervali iqneba:
2 2
(88.42 80.61) 1.96 5.62 /50 4.83 /50 a1 a2
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