Binomia X Quaatile Ths
7&naTA
Lshara e
In
30. 12. 2022
kuainaas anallics ua tan oma acTOAA 4CAnarioa
howa a Aat } inepmoamt dishotomun ( kinan
tril wth ouccaA pTobilly p.[Vka Aucans qrolailty
may s n dilional aA a4 uu). Vha inomid &Quaik
tata
a
gonRna mahoda
drawing infonamea. Yagarolinp f.
dheAainfanuntl tackniqpau sa onwa Ony he
i'nomi dhatriktion and
1ils ana iid.
BinomilTat
a
Aaxia
aAAuma
Lad * Ja ta
that tha dichotomou
AucoAA
ypothaaiadPTosaki,
dieholomua tiial (id) undar a ivn
Conditin ahoa
LExamla Wa ih
6»d heter e
ATAPMA 4 ^ivam chaTadar/at'ca k
wawail
pataonay Loan ov nol
proba&:ll, tat
ga,
in tona
a
Wa
W
thta ofhaaia taglin prollan.
moyawa
mor
iTo 1ilad tasl
VA. H
i)
+}
Lower tailw tod
VA. H
F< *
:
ate.
Bino
misAuatla Tata
30.12. 2022
in) Uffar 1ail Lt
Ho:s*
VA,
H F >p°
Wa
Wo axamina anoh thaaa caM0'
Dala
E
olactin
Wa
osaava
n
indaandat triala.
Lril Yosulta in a AucaAs or failuna ahann Ge
AMccAAA/ailuna ana aaatly okaT Valla and all dh
LE ompla
Wa ane tstip Elaelrenic Voti Ma cinn (EvH).
EahEvM loatd may ba afactiva /non-dafacti. Hpsa
il may not Aa aaay lo ktarmina, Hara ahEvM bunp
tot ia a trind
Lat thene2 sa n tidA
Lat tha numbar of AuccaAms da O
Aha mumbsar
alu
O,n -0
Tot Statiatie : Wa u
as tha tatt atatistic.
Nu
T:
0,
#AuccaAAaa)
Diatrillim: Neta that T o A a sinomil
diatribtion. For exasla, if EVMA anL manufactuna
theAama pTocaAA
uhana a h ma ina
ia
dofadiv
BinomiakAuaila Tiata
30.12. 2022
othProlsAibtzaindafundaally a tah ohar,
(n, p)
Bin
T
ohan
wa
tha
howa to4tad nmachinss (EvMA)
Undar nul pothuaia 4 ia tha. shaoihiod prokak:ltg.
So,
amd
tha
9latslaa
out
apropriate
naad lo fnd
cenadruct tha erlicad ragions
dislsibtion oith paTamtTA
Lat
ua
diz
uninp Binomial
amd
ha hraa tosl
now axamina
n.
scanaTiDA.
Hypohesiaodinp
Casai)
H V. H
#°
statiatic FB
TBin (n, p*) undar Ho
Nota a t
Notie hat
our
tat
the eritical
Tgion o daaind
,
aiz f
o tha wp taila 4 ha nl
EAAi,
wa
hwa Lo
atibutup T
find wo pointa 1,
coTpon
nd t2 aud
Lhat
PTS) % art KTS
and P(Tsi,): | - /2
AA Tis disctal, o
may ns
alla to find t, and t
hainkyigr Du ouation , ia., 4, 2 t stiafyir
enuatioaa m
n
exiat
tha
30.12. 2022
Binomial usabla Tst
Ih we
wo nd t and
Jh
PTSt)» «
12
su
that
amtPTS-*4
mdP P(T<t2) : I-4
Suh n t t, apsroximshs tha. 2tpatilaand
aproximab, ha (1-/1) th matila.
9nhia
CaA
ha trua lava
m AyGen npt malh
Coneluwion
}aigni fican ca
exaclly
tha tast
Ret H, isf T
9n
On caAL
cAAL
or f
T>t2
tTS2,
hamaw no TAADn Lo
trua (or w do
baliava foror-doot thoat H,is not
no hom oanonph avidana to Tojet H.).
havuaia eicz te smalsr thaprolal
Comptation of the p. vaa
Lat
ta
okarvnd valu
Fid P
T "a)
TolA
t
nd
Thu
P(T> )
-van
2.
TToa
6}T
PT.4)
0
P(T. t)
min {,P.?
Binomial&Quatil
tasiouu
md hanca normal
(apuciall for lange
ApTeXimtin wane usd. hengh
daacrika
no,w
Binomid probI,
Computstion
Normal APPrOximalion
ene
30.12. 2022
Taste
normal
tha
it
ia
not
a
sroximatidu
naceaaity-
to Binomil
tsto
Not
Aiaa
that
T Bin (n,} ) , n koiy dha Aamfla
(numar f triale) Anad a
sucaas
probasalky
Aggetd
ECT) n
Hhe
m
V(T): n (1-")
Wa knos
TN(n7, n}*(1-p) akfroxinit.y
Lat he okarvd vebua. 6} Tka tola
Vhon
and
and
nr0
z<
t):P(
PT<
n(1-
P(
T>
to):
ohora
ohne 05 u uA
1
-
P(Z$
sn
S
nb(1-b*)
aa 'tontinuity corractip" that
impne va ha norma Toximation To Binonid
9 thoss tao prok.L:btinu ana f
Computa -vale as
2. min .
h.?
. roata etivda, tw
30.12.20 22
Binomid tQuutila Tste
Ca i)
Loar tail
hypothaaia to
ha
tat
ka tastad
ane
T(numlar aueaan)
valun
Amall
Nole hal
vala 4
(amadlar
is
folan
tond to indicata hat H,
avidanca
T provida lrongsr
W find
Region:
Critica
Consrualion 5
hat
an
t
againat Ho).
P(TS) =
Wa Tajact H, if
CR
Th
Combutatigm
o,
,2
hune
Jhina
As
AA
..,
iA
tf a
i'n his
coon
i
P(T$ toLawhn
olsevd numbar Me
toa
valne. 2 P(T:1)
T 8i. (n, p")
.
tha
p-vadua, may
wmA.
f
a
t.
Vluu
Nol hat vadna
ia
Aue CasAos
no.
oa
condutd
ha
ha noTmal appro ximatim,
Daily
p. Valna may
P T s ) :P(7<o-n+os
30
Binomial Quantila Td
) UWþar
Ca
Sinilarto lon tail tt. lft
TalTt
uantila. Tst
20 22
a
oreraine
Hero w coiah to taat shathar o
nubar z* may a
conaidard to be tha b th puaotila
oapopulation.
Hypoeaio ,
infananc
hua,
Aa uanltest o a tryiy to mab
aoul the }" th smanlika 6
Wa
a pépulation.
easontialn makin in fanan
ane
ca
bout
rosab:litia
and P(T<
PT
1
-tohanaT Binn, +*)
And
LNota ha
a
Cohem
z7
ia Cha47 th y
ho
Tandem Vatialla T,
P(T 2) <
And P(Ts z")>} 1
9uantila f
(9
31.12.2022
Binomid Quadlila Tt
pohasia oatinuad
CaAa i)
Tso tail Lt
ta fh per quartila
P(x4z)
A H,
z" ia
nat the
LEauivaaty, at laasl
P(x<) <
P(x 2")>*_1
and
s
ona.
or
h awonlila.
f tha top statamnta
P(x
s7*) > p7
i
floa
twe tast aLatistica, Aay
Taot Statiatic Wa oill
hia tord. and T ara definad fllooat
fr
T2
Tand
T
z?
T No. a Aanpl obarvations S
<z¥
vationa
obaar
No.
dampla
6
T
diacradtad ia the
Nota at tha nl hpo haaia ia
ua
aa
Moo ing caws
i)
T, io amall. ia ia rcausa under rkHo,
P(x )>". Jhug Amald Vauas T ond
diactadit kha null pohaaia
i) T
ia large. hia is ocaus under Ho
discradit tha null
nypthaaia.
Binomi
31.12.2o22
luoilila at
Tost Statiali: (lonli nud...)
Nota
f nona
m
T
ha sapla obsrvationa a4s
otarsiaT>
Nul Diatibution Ngta that hoth T ad T
2"
Count & Auc UA04 am okaarvalion bainy
a cout
aA ucara) f
or
<x*
n tndepndant Rarnouli triala
Undar H, bob Tand T
Bin (n, } )
Critian KogíonWa howa. aluad notad
Valun
ana
Tand larg vadu G} T
hat Amal
diaerndita the
null ypothaia. Wa, harapna, Procael to construet a
eritic
ragion f
oimRinf
Lat
T
Ai2a a
as
aa.
fnd andt
Bin (n, p*)
Wa ind a vama t Au
hat
P(TS) 2P(T-t) «,, auh that «, ia
t
Similar
cloAl to 2
oe fnd, a vaue t2 au
hat
PT42): 2?(T: 4) »1-«,
Auh hut a a
t:0
huA
Thud,td
ia
dmosl
aloul to 2
agu
t,
«. Both o, l
1
o, shoulu
31.12.2o22
10Binomias uadh Tut
Critial Rigion ( Gntinud..)
We
Toyaet
, if
akaad oboerud T<41
or
f
ooar vad T>t
Lh
iA
Ca Aa noTmal proximalion
ha mathod ahown
gi Vom
in
thesa
in
the saction
uAd,
fpr
tt
w
usa
Binomias tajts
notas
Computation / p vala
LA
obpa
s
and 0
Lat
0,
Computation f-Value
and T
Tz
sltiati. TTand
tuot
obav vauas h a
Lt
TBin(n, }*)
Computa
amd
Pl T40,)
O
Z
t
P(T02)
omple b-valua
RA
0
P(E)
PCt)
2.
min{F,,t?
31. 12. 2022
Binomisl hQuawilila Tuse
Hypotasia Tto
(Lour taildtost)
tast
taild
Cas i) O n a
P(x<")>*]
['H,:
z7
i s
a
ualila
H
>r" [H,: P(x<a")<F]
VA.
: aspudtla
ba t t ettiatic
in ha
Wa dafina T a a
ain Bin (n, *)
Now find 4
No
P(TSt)
mynet ku
praviouu CaA
2 P(T1) =d,
ht
ohaax, ia
eAd to
ta0
posaiLla
Wa
W Tjact H,
anch
to
that
fnd 4 an
T t,.
if obarns
aina)
Otharoiaa
cs
Ac a t Ho.
a
Computatian 4 valua: Compt
Lat a
oksaTvad vaua
O
pmpdo p-Valua as PTSO,) ZKt)
to
ohane
NotaAa
T
Bin
ufar
imilarly
n, )
taild tast
may
a
c a r i d Out