Tsu-2011 - ieeetsu

Tavi XIII
oramokrefiani amocanebi bernulis sqemaSi
HhipoTezaTa Semowmeba warmatebaTa albaTobebisaTvis bernulis
cdaTa ori damoukidebeli mimdevrobisaTvis
X1,..., X
n
da Y 1
,..., Y m
ori damoukidebeli SerCevaa bernulis kanoniT
ganawilebuli populaciidan Sesabamisad warmatebis ucnobi p 1
da p 2
albaTobebiT;
q11
p1, q2 1 p2; S1
Xi
, S2
Yi
; P1
, P2
;
n
m
S1
S2
i1
i1
n m
s1
1 n s2
1
p1
x
m n m
i
, p2
yi
n n i
; P P1
P2; n m
p p1
p2;
1 m m i 1 nm nm
nm nm
Q1 P; q1 p.
kriteriumi:
ormxrivi marjvena calmxrivi marcxena calmxrivi
H0 : p1 p2
H0 : p1 p2
H0 : p1 p2
an H0 : p1 p2
an H0 : p1 p2
H : p p
H : p p
H : p p
1 1
2
1 1
2
1 1 2
hipoTeza: H 0
: p 1
p 2
mniSvnelovnebis done:
kriteriumis statistika:
( P1 P2) ( p1
p2)
as
Z
N(0,1)
PQ(1/ n1/ m)
( p1 p2) ( p1
p2)
kriteriumis mniSvneloba T.V.: z
pq(1/ n1/ m)
alternativa kritikuli are C.R. ( H0
-is uaryofis are)
H1 : p1 p2
z z ,
H1 : p1 p2
z z ,
H1 : p1 p2
z z /2
an z
z /2
(sadac z aris N(0,1)
-is zeda -kritikuli wertili anu kritikuli mniSvneloba
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.
178