??.ogkbr 71 T-7

P(.F)= o ) P(s\'t

9l lVo n(*L c*€F?.

ry e8k -s 5z

I f evl e ur ?.. F |MAL ErAH I

*z

Pf'{,,rA2\; ? G,\ -t 7(arl - p(A,ttAz)

+ "€ qo*Si*r l-r,..haLe y o{_ r

rVlL, \'

Iyt

v! (*->..l J

e tay.-6 atcl4 ,

4 v1 J^'sF,^"l- . b-* g,

fr*e

(T)

tr)t - ?(b;)

!t!i'@\

S.&.P

9, = t-J ,,

f52 -- c+J rr

?[$,nb7\ =

?(B,vBrl =

5 ce.<Js

a*,h

. -49

P f&,1 =

PC$zl =

?(b,Iz

19.-Q

t?.& :

k'1 "&!li*t".-t-

I

t2-

PfD,'f + ?(nrl- ?fB,/tRz)

c\4. L"*hh {" .U "*h

b t: J &'sF

tt B)=

!6zr9rI-

iL

f,

(r^-a

No

c-ol

c-/^

rS

t!<-

11')

? CB,}\;-

rf)

? (6..1 =

b5'.

CrVsr 1.td1;A L ?Btfut$lLt 17

'l{.r^" -ir b**"1

fl(Br):

2 io ckr, 2 tue*.^!, I clrt4

(:)(7)(l))Ar^l

FTB \

o*1* r9

}Lj

B.

b'2

s

P(

(

l

fo9v

9t^tO\=

(r\. blt .f

.J ^: sQo&.

F(B'l = Pfi) P(arlA,1 erdgt+'/llx) t) t1 (r

EL tr So

=) Pf*o$\- Pf'{(s) ?Cb)

W o- 52 P9'7'1il L'k'

S,, '.a'r *.i r) te <Jr :' ? fi \ :

;*W,A'

(?tP(B)= ---

(:; )

t{.?e .'t

. w19S

DrSc&Er E-

g c\r)

Ff,) ?.J P

lr,rla L k-u l"-J& &&Ll

e:

T r\ r-l

?(A,ta\ =

--> T"r[ t ,% ,-l

A J,v-r, fi,* d7o

Lt- hoi- hrs

-7L, Pc- t. ,fI

|eh D: Jt!.'r.

P CB l+,) I (A,)

FrB(A ) ?ftil -y ?(ttAr) F({?J

J qLa-a€ - e'*ts

( & *v &', ,aat -

hrt .s e-1 e[,.-/

-t^ co t.-- olu W.n

(ec \.tl ts e I .

) bcf ^r-n";

f (-rP lD') = o) ot

f--J.t ff.t hal- rr P.lrh.

o.8o o.sd

-P g. eu.!ih^ .

,-7. p.- l.t'lt+Y "fV-t,ul,, uN\ ffi.l-

A Nn.,--e.^4

S":4, F;

':** r!

Tru

.- a', Za

\tJl-.rk

?IretO\- t- Pfr^,tD)

= s.8o

(o'l -- o,oQ )

P"-t. "p

?rDtYP \=

fP : t* r. e;br

pf rru tb'l

tatr1 o- Pr*** JPTTPID) TTD)

f

[:

R.v,

i:tt-,/t

-s>

J}

P(rtro) p(Dl+ pfrplui\ prD,)

"9pe

62:

o.f,a.o.sA + o.ot . (t-oo\

f(x:l = f l5=":)4

Z ?c*>\--lL at

zte

a [a-zylE&\--

Ff"r o,? o'5 o'5 o'L

I rrl o rr.t* c '{ r ls-Bt Du rt's r)

r=

a1 =

l.o,? + z'o.X-t 3. o,1 + Lt'o,Z

o,Zlo,6+o,q+o'3= 2'F

f *;, l(x;\ - Q. )Lrt= (

?zrv*rW l"t,.fa

Y! ZE,'J-:,

# + s.rccz^l*{ "f

?( Y=yl -- (; ) FY (r. P)"-' -r--.,ttl-,/

b (r, rlBrvo r-rr * L

L{31. ^ ? /

?bF

rJg Qk\-

V 6ta n9(r-e )

b* ?f ."_ g {",tr\ _.9 L

Y :- .ff .( r-- F5

f ( v )z)=

o.l

&Lt e 6 l"u,tlt^

.t

| - ?(Zet) = t- ZY;o

9,.rlr J.F..k occ-- o?

uG"" s) (..c S ) '

+-1(,..9) r-.tr)

( u= 6, ? --.., )

t 6-a("-r)'(".r)

b

(i\

*3r. n- t..( t{ '.'F to 8t rl" 4< 6*J

vr= 9 9.fh nr "a-4rr [- o k ruQ

L

p(z* [r-o*r.1r"t) - p(f, *z\= 2 (i)?'(,1)*-"7:b

U 96*'rtvE bt rronttL t, J I

v (11 --

Z = # 'F h"'o& ^'-'-l t"

>: A grc @r5 t*{i*-c,5 u*M'

Pr. t.\*(( '( J'P'-0 s rr P =

wh.! ,! 1..unVk\ ilL 9n

?(+-nf = (i)t

PC"a-s)= 2 (*"-')?

=-<

tqee)tL's*E<rLtc PDF

( *.-,t ) ,"(,-r)*-t *--z-P' r+(r -'

-! o.r*a 0k t-'C 't4rec''{A '

6..rt- J.Feof-i-t ltr^ rt g e. t.e,N

o,o S

P,+il 1.,-4 7

l// = # itt,t^, t^ Ptttk tt rb*54N=t{,!N2

Perrlow ?DF

3- , * 'f ''"-ts/ F [aq"l ha'P?-3 o+ a

tr , 6t r* r.o 1r o-*-lr'l 1 H a *r P '4

P(vl= +n P -- | ,nl-

E>.

oli a.t S -

P(r,u=,.) ' (Y')(J-'^)

e 'i'" )

F.?"*s (4 J.' 1t '1 c ecag n o*t "{

fr E '# P('o'tr '-" looI \7 -IP(r'r\' Z '\'''. Yl

Z3r,

uz= o)rl -'-

e evtl 4 +-rp/ s ec 4 , o'**-'1 #'-l-

,*lr l-;/f,eot ,. -'lkl-

6t: I

t ta ?ao t(' f-tr

'('Fol

\ z t"S

\tv- Pot*r- €J f

I-lu,thvo., .te 0,e crck y- v,

f f*,y\, P(q^r7.,"/l

(r\: Z rwrlY '/

/^z = Z-F,6)x/

F,

., a< (-B \ = ( {,-nr)'[, f*,

62, z c.v (I, *c \ a

(',2) €6

Vrcvt=2 tc*..,).x

A-= Z 7 t"cy)n

b> ?tr,z)'N,all"k)

3 z-a

uee ff) = 7 tt',nrf tr',)7

7 : C*-Aa\ (, - l r) Fa' " )

-L*., \e &

6il6E 6z

rt/4o61^4tL PO P

9=

3,3 -*

3,? t*l*g

,{b9?

:\ ( B,F g=r +t ', t 'r*?.)

v br W = Qo ro, j *..E

b,^,= &o+orlU*o'l-,

61., = n,' oj < ,; s; + *,o.l.t"i

e

cl^ .s€

U , c.rr71-Levo eJ tc.w

?(t+3etl -

Ex orr Fopzr P,D,F.

Ei**.'-.j- e[a)'

v,(R.((,"ce "-.e ['P) =

G 1-, rrrlorJS R.V,

nb

), cat t"

Q64 =I

t-.t

* l*ak)l- :

,, e Cl$

[* Far l-"fu r.v)' P \ r? fr*l Jr-

JL- la

e: ur,r Fo cn

(s S4r Prob. # t

P,DE .

TasF # j

r)- -u b't q,L/ 6'e b)'IL

M.'<;el ?.Df,.

rre** = y,

, Ff*r = #"v&:7-/ce o 67

? ( 7!,< ?..s(.' r( Rrvie.v Qvr* #3

(s#') *-6ft.e.< I

? (u z ? .'b\ =,

p._ t .o<'. 3.L_T

) = ff('#) -+! \,8 hR.4

(r .!a.

?o"*hh f"1 y?;,F. 1(Z=x.g)= fI

P; o,4F r( E-/t6

€> ?( * s

ra

E OEp l$k7-r t#r\", €*'?*hte 0.1ry, !"hL*

Fcr\c

8"" o"t,f

-+ 7p. r-6ug

::?*- r.6r r-6-

:) >-e -e u 6A9- 6 *,1*

x

tzG }r2c t= F, 6"= 9'

o Drstit!"t s "1 r.*t 1.r^<,,-t{.

CL.q

5 "*91.X fl e*

5An?tt^, o'

.n_; = a .4,*,

e(9\-- / ,

Tetlr *)

? ( zz z jc-5.7\ a

cg rrvl,,*L Li1.-r Tffft

ot EtrA.t guvt. 4

tuQoa E(E;\=1,

ue"(f l= t't4

7. ru(srt)c/,Ji

Y s.a$ an* gA* 5-e[

, *) F. J,ctrr,L-f,' F C* r =

t 36/*Z--7, Cg= A. =5

?('''-'z?< 'l'\.rL\r\rr7t

"a " (s.-i )= 6?

i -t

(. Rr.s. z I ,. 12 q=- L1

.r6 [.,e]

)^i: =9,

0f".6')-P (-",)

h!-^ ***,(

L6

-)L e-t - I6f='rzt-i

c.{?Lbe^/co tNT g-pvAo g^ r.eAa

IF (5;) to vsRal( oD^ , R^t +6? kn'*

f P bf) .* ^,ofA{t- *c" u^kn*

I o 6';),()l) !ue(!t , u'',6) .*k*o* v{'qJ

Cou? rDg,,ce 'f t{q?kvlc 1^ PP.o 9514st'^'{

{)_

r-!(t-;)

(.- t

?

?.-?z

b,^*-.L bU,?|, ^ L+

bl...J / (1 t r'{r l- + /Y,(;,-

C.r1,rF ,6Pzv cR "l cl.ff?.t>t*'c t w*ll*{c*l

I+\,t-

1\^.1

?(\\

1?r;)

[-f"-,\ 62

Jn;'(,^-rl Jt -l)fr;".,))

aesT s 4

ll* ?(41

rtl f oTflP515

,g 6 t5 k^--t, lrV t (* ', ^ -, ) ' fl^r^'*'i rr

Iesfs of hypotheses

Hypotheses Rejection Region of ,EIs

HoiF: po

H1: p. ) ptu

Hoi p : ltoH1: p" ) 1L.o

Ho: Pt : ltzH1: p., ) 1-t,

Ho: Pt : ttzHti Ft ) ttz

Ho:P: Po

H1:p ) po

Ho: Pr : PzHr: P, ) p,

Ho: Fr: FrcHt: 9t > Frc

x-llo- > z(d)

olYn

i-u,,---;=r(o:n-r)s/Y n

i-7 > z(o). /--/ tv oil nl + oiln2

yln - po

x-y> t(o;n1 t n2 - Z)

l(n'- l)s,'z+ (nz-r)i f t 1\t-T-,Y r,*nz-2 \nr nz/

> z(")

ytl\ - yz/nz

- - \*,i

l(*r#;X'- t+)e.;)h- Brc - t(o',n - 2)

l>0- trta, - r)v 21'' - '-Y

po\ - po)

n

Tolerance regions

With normal assumptions, - t ks covers at least (100)p percent of the population withprobability 1 - a.

d[,

,ol

{E + t:cu Nc + a:d

e)4Are: -IJO,yig: -Il-I:U

azv + {:x

sueqc loquo?

Q - u:7ln)tarj

(z -', + ru'.Z/p)t + { - L

Ql4z+,(-L

(ro'xrg + odhu

eBtelzY'rY

suotlnqrJlsrclIerruoutg luapuadapul

a3rc1u(d'")q 1erruourg

suorlnqrJlsrC[ luapuedapul

ua\ou{un z,('o ''t1*

u1(ou{ z,a?nlu rc (ro'rl)61

lenba lnqumoulun !o'jo

suorlnqrJlsrclleruJoN luepuadepul z7l _

aBmlzY'tYumou4lo'!n

rfl

Zy ly Ar _/\ .,

(zu lzt - t)(zu /zt) (tu /tt - )|u lt,qlIzy ty

lzln)z+-*- - . .A tt

Qt")z + I/7u ru\ Z-zu+tu A

(r.r/@'"

zd-td

Zd _Id

rt

rtt

uL-, kl")z + r

II

I'

I

I

i

,l

!a - u:7ln)t + x

Q-")lr({-/{)K

@lr - r)@lt)

suoudunssy ralarrrBred slurodpug

qeNaw! acueplpoc

1T1 1--l vr I \_/, It