Tsu-2011 - ieeetsu

SeniSvna: saSualoTa Sesaxeb tolobis Sesamowmeblad T kriteriumis
gamoyenebamde winaswar unda gamoviyenoT F kriteriumi, raTa gavarkvioT
aris Tu ara dispersiebi toli. am ukanasknelis gamosayeneblad ki aucilebelia
populaciebi iyos normaluri an daaxloebiT normaluri.
satertvaitis (Satterthwaite) meTodi
X1,..., X
n
da Y 1
,..., Y m
ori SerCevaa damoukidebeli da populaciebidan,
romelTa dispersiebi gansxvavebulia.
hipoTeza: H 0
: a 1
a
2
0
mniSvnelovnebis done:
( X n Ym
) ( a1
a2)
kriteriumis statistika: T ,
'2 '2
S / n S / m
( xn
ym) ( a1
a2)
kriteriumis mniSvneloba T.V.: t
'2 '2
s1 / n s2
/ m
Tu mocemuli mniSvnelovnebis donisaTvis T statistikis dakvirvebuli
mniSvneloba t akmayofilebs Semdeg utolobas
t[ c].
/ 2
t t[
c].
/ 2
,
sadac [] c aRniSnavs c ricxvis mTel nawils, xolo c gamoiTvleba
Semdgi wesiT
'2 '2 2
( s1
/ n s2
/ m)
c
,
'2 2
'2 2
( s1
/ n)
/( n 1)
( s2
/ m)
/( m 1)
maSin mniSvnelovnebis doniT H 0
: a 1
a
2
0 hipoTezis uaryofis safuZveli
ara gvaqvs, winaaRmdeg SemTxvevaSi, mas uarvyofT.
1 saimedoobis mqone ndobis intervals aqvs Semdegi saxe:
( x
n
y
m
1
'2 '2
'2 '2
t[ c].
/ 2
s1
/ n s2
/ m,
xn
y t[
c].
/ 2
s1
/ n s2
/ m)
m
.
magaliTebis amoxsnis nimuSebi:
magaliTi 1. fermeruli meurneobebis saSualo farTobi indianas
StatSi Seadgens 191 akrs (1 akri = 0.4 ha), xolo aiovas StatSi ki 199
akrs. davuSvaT, rom es monacemebi miRebulia Sesabamisad 8-isa da 10-is
toli SerCevebidan da Sesabamisi Sesworebuli standartuli gadaxrebia
38 akri da 12 akri. 0.05 mniSvnelovnebis doniT SeiZleba Tu ara davaskvnaT,
rom fermeruli meurneobebis saSualo farTobi am or StatSi gansxvavebulia?
igulisxmeba, rom populaciebi normaluria. aageT 95%-iani
ndobis intervali saSualoTa sxvaobisaTvis.
amoxsna. winaswar SevamowmoT hipoTeza imis Sesaxeb aris Tu ara populaciaTa
dispersiebi toli. CamovayaliboT ZiriTadi da alternatiuli
2 2
2 2
2 '2 '2 2
hipoTezebi: H0 : 1 2
, H1 : 1 2
. am SemTxvevaSi 38 s1 s2
12 . Sesabamisad,
Tavisuflebis xarisxebia: 8 – 1 = 7 da 10 – 1 = 9. amitom kritikuli
2
.
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