Tsu-2011 - ieeetsu

Tavi VIII
ndobis intervali da hipoTezaTa Semowmeba
Tu hipoTezis Semowmebis amocanaSi xdeba nulovani hipoTezis
uaryofa, maSin imave mniSvnelovnebis donis mqone ndobis intervali
populaciis parametrisaTvis ar moicavs parametris hipoTetur
mniSvnelobas.
Tu hipoTezis Semowmebis amocanaSi ar xdeba nulovani hipoTezis
uaryofa, maSin imave mniSvnelovnebis donis mqone ndobis
intervali populaciis parametrisaTvis moicavs parametris
hipoTetur mniSvnelobas.
magaliTebis amoxsnis nimuSebi:
mgaliTi 1. Saqari dafasoebulia 5 funtian (1 funti = 453.6 gr)
fuTebSi. kontroliors eWvi aqvs, rom fuTaSi ar aris 5 funti Saqari.
50 Saqris fuTisagan Semdgari SerCevis saSualo aRmoCnda 4.6
funti, xolo Sesworebuli standartuli gadaxra ki 0.7 funti.
0.05 mniSvnelovnebis doniT gvaqvs Tu ara safuZveli davaskvnaT,
rom fuTaSi saSualod ar aris 5 funti Saqari? aageT 95%-iani ndobis
intervali WeSmariti saSualosaTvis.
amoxsna. CamovayaliboT ZiriTadi da alternatiuli hipoTezebi:
H0 : E 5, H1 : E 5. am ormxrivi kriteriumis Sesabamisi kritikuli
mniSvnelobebia: z
/2
z0.025 1.96 da z /2
z0.025 1.96 . kriteriumis
mniSvneloba iqneba:
x E
4.5 5 0.4
z 4.04 .
'
n 50 0.099
s / 0.7/
radganac 4.04 1.96 , amitom nulovani hipoTeza unda ukuvagdoT,
anu Cven gvaqvs sakmarisi safuZveli, raTa davaskvnaT, rom fu-
TaSi saSualod ar aris 5 funti Saqari.
avagoT 95%-iani ndobis intervali saSualosaTvis:
'
s
x z/2 E
x z/2
,
n
n
140
'
s
0.7 0.7
4.6 1.96 E 4.6 1.96
,
50 50
4.4 E
4.8 .
rogorc vxedavT, 95%-iani ndobis intervali (anu ndobis intervali
mniSvnelovnebis doniT 0.05 ) saSualosaTvis E ar moicavs
saSualos hipoTetur mniSvnelobas E 5.
magaliTi 2. mkvlevari amtkicebs, rom specialuri dietiT gamokvebili
zrdasruli Rori saSualod iwonis 200 funts. 10 aseTi
Rorisagan Sedgenili SerCevis saSualo wona aRmoCnda 198.2 funti,
xolo Sesworebuli standartuli gadaxra ki 3.3 funti. 0.05 mni-