n'nU':1 nu,!)ni1:1 P -'.II

in~N(P,:q)

Ho :P ~ Po :tJ'P11:1.1

H] : P > Po

~C =Po+ ~ Z]-a :n""'Pi1 i111P3i1

P > Po tJ'P'Un1 Ho m~tJ'n11 ,a n"':1

:1:13:>

-

.X ~ C tJ',:1j7n tJN

Ho : P ~ Po :tJ'P11:1.2

H] : P < Po :1:13:>

~C = Po - ~ Z]-a :n""'Pi1 i11'P3i1

P < Po tJ'P'Un1 H 0 tJ'n11 ,a n"':1-

-

.x ~ C tJ":1pn tJN

Ho :P =Po :tJ'P11:1 .3

HI :P =#Po :1:13:>

P =#Po tJ'P'Un1 H 0 tJ'n11 ,a n"':1

i > p, + ~ Z tJ',:1i7n tJNn- 0 r a I'" n ]-z

X- < D - ~ Z tJ,I..:1i7ntJN 'Nn_ro r a "1'" n ]-z

:np'1:1' ',n'3'ni1 tJ:l1ni1 '11:1 .4

Ho :P =Po

HI :P =~ :1:13:>

:i1'i1',tJ"1~' a,p '1:1»

n ~(

~ ZI-a +-JP:i:Z]-P

J

2

Po -~

nn}lWi1 ni7I"T:J.DDIO

'~N:>n',n,u nU,!)ni1:1n,n1n, .Ii1»11'nm~i1

-

((Y2

JXn~N Jl,---;;

H 0 : Jl ~ Jlo :i1'»~i1 tJ'P11:1.1

HI : P > Po :1:13:>

(Yo

C = Jlo + ~ Z]-a :n""'Pi1 i11'P3i1

P > Po tJ'P'Un1 H 0 tJ'n11 ,a n"':1-

x ~ C tJ":1pn tJN

Ho :Jl ~ Jlo :tJ'P'1:1.2

H] :P < Po :1:13:>

(Yo

C =Jlo - ~ Z]-a :n""'Pi1 i11'P3i1

P < Po tJ'p'un, Ho tJ'n'1 ,a n"':1-

x ~ C tJ":1pn tJN

Ho : P = Po :tJ'P'1:1.3

HI :P ;;j::. Po 1:1):>

P;;j::.Po tJ'P'Un1,Ho tJ'n'1 ,a n"':1- (Y

Xn ~Jlo + ;-Z a'" n ]-z

- (Y

X n ~ Jlo - ;- Z a tJ":1pn tJN m'" n ]2

np'1:1' ',n'3'ni1 tJ:l1ni1,'U .4

Ho :P =Po <70

HI : P =Po <711:13:>

:i1'i1'tJ"'~' a, p '1:1»

n '?

«

7oZI-a + <7]ZI-P

)

2

PO-PI

tJ',:1pn tJN

h'tJi)i1 bNl1P

Cov(X Y)= L,(Xi -xX~ -y) L XY --, n = I I , -X.Yn (covariance) tI~tI'\Ut1 tI,),\U

cov(X,y)r=SxSy

r-Jn-2

~ ~ tn-2tlNtlt11'1 tI"1't1

Y = a+bX

x =a'+b'Y

S;.y =S;(I-r2) 1'1"0..,)..,11'1' fI',,\U

. Ii!J')~'72'n O1u,::I:! il~p\ljil = X : Xt))l"t. rfj,:>;jj Jijjjf)j j!)~n-<= Y

cov(X,y) = 466.667 cov(X,y) =0.99r= SSx y

Y=a+bX b - COy =0.007- 2Sx

a = Y- bX = 2.8

I' = 2.8+0.007X S;.x =S;(I-r2)=0.069

X =a' + b'Y b'= co~ = 140Sy

-a'=X -b'Y=-380

X = -380+140Y S 2 -('2(1

.2\-' 3 '1""""'"1x.y - c}x - f )-! ,,-0.0 I

1 1+ rZ - -In-

-2 l-r

Z - fJz ~ N(O,I)(}z

: .,~.,)) , HI : P > Po .,))) Ho : P = Po > 0 tl1".,:1,

1

(}z= .In-311'tl""\1'0'

1 1+ Po--In-/lz - 2 1- Po

"~""tI tI~

Z - ll"> ~

0 '--.::... "'I-"(57

aN a 12"1:1"~Nft n1~~i1 nx f1n'u

z =~1111.992 0.01

. HI : P > 0.7 I:\D Ho : P = 0.7 : ;".-,::U r;~"nv11 X1:iWf:l.:Z't~)""

.. - 11 1.7 - I 20 - fJz - 3 08'1 - - '1 58r z - - 11- U z -

.J3- . ~ > "'0 9"5 -~.

? 0 3 3..7.

- . Uz

1

cov(X,Y) -x y \U 1'1'O")"1'1'1'b= a=Y -bX

S2x

S_.X =S.(I-r2) 1'1"')"'f1 '1' nu,\U

cov(x,y) -y x \U 1'1'O")"1'1 '1'b'=

S2 a'=X -b'Yy

X: 400 600 1000 200 600 &00Y: 6 7 10 4 7 8

X = 600 Y=7 S; = 66666.667 S; = 3.33

. p > 0.7 ,~ '/"'0)'I "£)N1'\SI"')J~1'\ SIN1'\n.,) 0.005 SI'i'n:.u.1 Slt.)..,:.

1V~tI - tI'~"~"

Y=a+px : il')tJ1,:>nO

Y =a+bX :C)1n:l

S~.X = S~(l- r2) 82 =~S2 =~S2(1-r2) .y.x n-2 y.x n-2 y

~2 2(

2)~2 Sy.x Sy 1- r

Sb = - =nS; S;(n - 2)

b -: f3 ~ tn-2Sb

s; =s;(Lxnn

a-a

S ~ tn-2a

~2

(

1 (x _-:-:\2

JSy(xu) = 1+-+~ S2n nS2 y.xx

Y -yXu Xu ~tn-2~

S y(xo)

: 1- a '\lj lntJ lln1:l fJ -, lntJ n111: )N:>n1

~ ~

b - Sbt a :$;f3 :$;b + Si an-2,1-2 n-2,1-2

: 1- a ,\lj lntJ lln1:l a-' lntJ n111

~ ~

a - Sl a :$;a :$;a + Si IX

n-2,l-2 n-2,l-2ill

L

: 1- a '\lj lntJ lln1:l ~o -,lntJ n111

~ A

yx -S y t a:$;~ :$;yx +S yx t a0 xO n-21-- 0 0 0 n-21--

, 2 ' 2

2

nV)A;1~:n" 1':1 1'Up

z=X-j..la/-m. ~ N(O.I)

x ~ N(j..la2 ), n z~ N(O.I) (1

(n-l)s2 L:j(Xj - X)2 2~= 2 ~ X(n-])a a

XT =z2 (2

.n"] Xi ~ N(j..l,a2)

z =ten-I) =

{fii 2)~

(n-l)

X-j..l

a/-m.

(iN )s2

(~l )a2

X-j..l

= sNIT(3

u~ X2

n"] < (m-l)V ~ X

2(n-I)

(4

u/(m-l) x2(m-l )/(m-l)Fm- \,n-] = =

v/(n-l) x2(n-l )/(n-))

~ "2 "2( -1) . ~ ~(m-) a2 s2- 1_--2

- "2 2~.~ ~(n~) a~ ai

1F]-a.m-I,n-I =Fa.n-I,m-I

:O))pnD "(5

FIO,6,.95 = 4.06 :il):n!1J

F6,IO,.O5 =4.b6 =0.2463

XTIl z2 2 2F I n- I = = , =t( I) ~ z, 2 2 n-

X(n-I )/(n-]) X(n-] )/(n-I) n-700

(6

2FI,n-1 =tn-J F = z2

],00

nn)J\!JilJJDn] (7

(

al)

2

2 2 Ho: - = 1Ho: aj =a2 a2

2 2=>

( )

2

HI: aj =a2 HI: ~~ > 1

"2~ > Fn l-I n2-1 I-a :O))pnD ON a D"l] H o om!1"2 "S2

llP)A;I~;ni1 1':11VP

z=X-j.laNn ~ N(O.I) x.~ N(j.l, ~12) z~ N(O.I) (1

(n-I )s2 Lj(Xj - x)2 2~= 2 ~ X(n-])aa

XT =z2 (2

.n") Xi ~ N(j.l,a2)

z =ten-I)={X!ii

2)~

(n-I)

X-j.l

a/-ffi

(~ )s2

(~l )a2

X-j.l--s/-ffi

(3

u ~ X2

n") < (m-I)V ~ X

2(n-I)

(4

, (~-I) sf s2

Fm-] n-] =u/(m-I) =x2(m-I)/(m-I) =cmsv. ~ - s~

. v/(n-I) x2(n-I)/(n-l) ~ . s~ aT. (n.).) a2 ~22 v2

1FI-a,I11-I.n-1 = Fa.n-I.I11-1

:o"pnD ,,(5

FIO.6..95 = 4.06 :I1D)n')

F6.IO..OS= 4.66 = 0.2463

XT/1 z2 2 2FI.n-l= 2 = 2' =t(n-I)-7Z

X(n-I )/(n-I) X(n-I )/(n-]) n--700

(6

2F].n-I =tn-I F = Z2

1.00

m,~-'!)_jLnDn) (7

(a]

)

22 2 Ho: - = 1

Ho: a] =a2 a22 2=>

( )

2

HI: al =a2 HI: ~~ > 1

"2~ > Fnl-I n2-1 I-a :O"pnD ON a D"I) Ho o'nn"2 ..S2

: (l-a)% lDtJ-nDl) (~~t -) lDtJ-mn (8

Fnl-l,n2-1,!X.~Fn,-l,n2-1 ~ Fnl-l,n2-1.1-!X.2 2

F J~:)' < F

"-I,,,-I'T- (~;)' - "-l,,,-l,l-T

(~rFn,-I.n2-1,1-!X.

2

<(

Ql.)

2 < (~r- a2 - Fn,-I.n2-1,!X.

2

:p))

.a; m))))\U 0)1 m))Dl)) m)tJ)):m.m nj )1))) nil) O))NlPN O)D::\1D )\U m))))\U 1il sf

:ilmn

F9.7..99 = 6.72

F7.9,.99=5.61

A

Sl =0.5A

S2 =0.7

nl =10

n2 =8 .::

:iVil) (~~t -) 98%)\U lDtJ-m)l

0.25/(6.72) ~(

Ql.)2 ~ 0.25(5.61)

0.49 a2 0.49

0.076/ ~ (~~t ~ 2.862

.)II)il mn) N~m Ql. = 1 :ill)lila2

L

r'I""JiU tJPU'£:I31i1j. m,rntJ ,tJ\!J tJNn\!JiI

.J"~n:rl)) Jl))£)JlD JlnN )) ,m)l.:»)))N 2 nmm

x ~ N(~x,cr~) ==> xn, ~ N(~x,~~ )

(

2

)2 - cry

y ~ N(~y,cry) ==>Ynz ~ N ~y, 02

:m)))Jl )Jl)J m)tJ))))N 2 ,'lJN) (1

~2

)cr2 cry

X-Y '" ~x - ~y,°~ + °2

X-y - (~x - ~y) '" N(D,1)z= 2

cr2 cry---X+-°1 °2

:il)il) 1 - a 1DtJ-JlD,J ,~x - ~y -) 1DtJ-mn ,IN)m

x-Y-cr~ cr~-+-°1 °2 Zl -~ ~ ~x - ~y ~ X - Y +

2

2 cr2crx + -L . ZI _!!.0 I 02 . 2,

O)lDil nm'lJ JlN onD ))D )JjJ) , i7JJ1i' N71 i71H!Jm))'lJ 0)' m)))Jl )Jl)J Jl1'tJ))))Nil 2 ,'lJN)

:)11)' cr2 -) ,£))'lJD l1mN )JP) )))jJ)'lJ )11)' Oil))'lJm s~, s~

(2.

"2 "2

s2 - (OI-1)sx+ (orl)syp - °1+°2-2

x - y - (~x - ~ )y '" t

~ 1 1)nl+nz-2

sp - + -nl nz

:il)il) 1 - a )'lJ 1DtJ-JlD,J (~x - ~y) -) lDtJ-mn P))

- - AGI 1) . < <- - AGI 1)x - Y-y sj5\i1;+ nz tnl+nz-2.1-~- ~x - ~y - x - Y+y sj5\n; + nz tnl+nz-2.1-!!.2 2

. dj '" N(~d,cr~), dj = Xi - Yi )II)' m)JlilD ,\)£))) ,iln il~ tJ"1717 (Xj,Yi) ,'lJN) (3

d-~ '" tn-I. Sd/-Iff

"2 -:onp 'Sd m))'lJ) d )'~mD 'lJ) d1... dn il~np)

I. I

I:1) ilN,) 1 - a 1DtJ JlD,J ~ -) 1DtJ-mn

" "- ~ - ~d--t ll a~ll d ~d+-t II a

-Iff'11- . --,-- -Iff n- . --2 2

-"'--'" ;::;;:s:;;:;; ~ ..,