Uji Hipotesis Adi 2

7/25/2019 Uji Hipotesis Adi 2

1/50

STATISTIKA INFERENSI :

UJI HIPOTESIS (SAMPEL GANDA)


2/50

Outline

Uji Hipotei !"#i"ni $en%"n "&pel%"n$"

Uji Hipotei Me"n $en%"n S"&pel

%"n$" : ' Uji tuntu popul"i "lin% e#%"ntun%

' Ujizuntu popul"i "lin% e"

' Uji tuntu popul"i "lin% e" ji"

uji'F &enunju"n *+ ++,

' Uji tuntu popul"i "lin% e" ji"uji'F &enunju"n *+ - ++,


3/50

Uji Du" !"#i"ni

Prosedur Uji Dua VariansiD"l"& uji $u" ."#i"ni ini ."#i"ni "&pel

(+) $i%un""n untu &en%%"&ilei&pul"n &en%en"i ."#i"ni popul"i(/+),

J"$i $"l"& uji ini $i"&il uji "&pel "0"

$"#i $u" "&pel popul"i1 $i2itun% ."#i"ni$"t"1 $"#i &"in%'&"in% "&pel $"n2"iln3" $i%un""n e"%"i $""# untu&e&"n$in%"n ."#i"ni popul"i,


4/50

P#oe$u# $"l"& pen%uji"n $u" ."#i"ni &en%iuti

l"n%"2' l"n%"2 3"n% "&" epe#ti pen%uji"n

"&pel tun%%"l 3"itu e"%"i e#iut :

Pen%uji"n Hipotei nol $"n Hipotei Alte#n"ti4,

D"l"& uji ."#i"ni 2ipotei noln3" "$"l"2 ti$""$" pe#e$""n ."#i"ilit" p"$" e$u" popul"i,

Se$"n%"n 2ipotei "lin3" te#$"p"t pe#e$""ne#"#ti "nt"#" e$u" ."#i"ni popul"in3",

Ho : /*+- /++

H* : /*+/++

: (/*+5 /++)

: (/*

+6 /+

+)


5/50

Pe&ili2"n tin%"t epentin%"n

(level of signicance) 7,

Penentu"n $it#iui pen%uji"n 3"n%$i%un""n,

D"l"& uji $u" ."#i"ni ini 3"n% $i%un""n"$"l"2 $it#iui F 3"n% &e#up""n u"tu

$it#iui "&plin% $en%"n i4"t'i4"t e"%"ie#iut :

Dit#iui F "$"l"2 $it#iui "&plin% untu."#i"el +*8 ++(rasio variansi sampel)

Selu#u2 nil"i F6 9

Ti$" i&et#i,

Te#$"p"t pe#e$""n entu $it#iui 3"n%te#%"ntun% p"$" uu#"n "&peln3" e#t""n3"n3" "&pel pen%"&"t"n p"$" "&pel

te#eut,


6/50

Nil"i'nil"i $it#iui F tel"2 $i"ji"n $"l"& t"el$"l"& entu F71$4*1$4+ 3"n% $"p"t $itentu"n

&en%en"i ti%" 2"l e"%"i e#iut :

Tin%"t epentin%"n (level of signicance)1 7

De#"j"t ee""n (degree of freedom) untu"&pel 3"n% $i%un""n e"%"i pe&il"n%

$"l"& #"io uji +*8 ++1 ($4*- .* - n*'* ),De#"j"t ee""n ( degree of freedom )untu

"&pel 3"n% $i%un""n e"%"i pen3eut$"l"& #"io uji +*8 ++1 ($4+- .+ - n+'* ),

S"&ple $"l"& ."#i"ni 3"n% te#e"#$in3"t""n e"%"i "&pel * $"n el"lu$ij"$i"n pe&il"n% $"l"& #"io uji,


7/50

Pen$e;nii"n $"e#"2 penol""n "t"u$"e#"2 < $"e#"2 #iti

Pe#n3"t""n "tu#"n eputu"n (Decisionrule)

Pe#2itun%"n #"io uji (RU)

Ru&u 3"n% $i%un""n untu

&en%2itun% #"io uji (nil"i F) "$"l"2 -RUF - Ftet - *+8 ++1Pen%"&il"n eputu"n e0"#" t"titi,

Ji" nil"i uji t"titi e#"$" $i $"e#"2pene#i&""n &"" 2ipotei nol $ite#i&"$"n ji" e#"$" $i $"e#"2 penol""n&"" 2ipotei nol $itol",


8/50

=onto2

Untu &en%et"2ui pen%"#u2 pe&e#i"n "2"npe#e$"& u"#" u"tu o&p"#te&en en$"#""n$en%"n $u" jeni "2"n 3"n% e#e$" A $"n >&"" $il"u"n u"tu pe#0o""n pen%uu#"neu#"n%"n eiin%"n $en%"n &en%%un""n

$eteto# un3i,

Tuju"n $"#i pe#0o""n ini "$"l"2 in%in&en%et"2ui "p""2 "$" pe#e$""n ."#i"ilit"

3"n% e#"#ti e$u" "2"n te#eut $"l"& 2"l&e#e$"& eiin%"n &en%in%"t 2"#%" e$u""2"n te#eut "n%"t j"u2 e#e$",


9/50

Di"u&i"n "2?" &"in% &"in% "2"n""n &en%2"il"n u"tu pe#e$"& $en%"n$it#iui no#&"l untu &en%uji te#eut"2"n A $ip""n%"n p"$" @ o&p"#te&en$"n "2"n > $ip""n%"n p"$" &oil'&oil3"n% ejeni,

Setel"2 $iuji te#n3"t" A &e&e#i"npen%u#"n%"n ee"# B*1 BC1 91 1 @1 1*1 B ($>),

Se$"n%"n "2"n > &e&e#i"n pen%u#"n%"neiin%"n ee"# C1 1 @C1 91 1 @1 +11 ($>) $en%"n &en%%un""n uji $u"."#i"ni ei&pul"n "p" 3"n% i" $i"&il,


10/50

Untu &el"u"n uji 2ipotei &ul"&ul" $il"u"n pe#2itun%"n $e#ipti4

te#2"$"p &"in% &"in% "&pel 3"n%&en%2"il"n :


11/50

Uji 2ipotei $il"u"n $en%"n l"n%"2'l"n%"2 e#iut :

*, Hipotei :

Ho : *+- ++

H*: *+++

+, Tin%"t epentin%"n 7 - 919 - ,

C, Pen%uji"n &en%%un""n Dit#iui FB, K"#en" ."#i"ni A lei2 e"# $"#ip"$" ."#i"ni "&pel > &"" n*-nA-@

$"n n+-n>- e2in%%" $e#"j"t eee"n

$4 untu pe&il"n% "$"l"2 $4*- .*- n*'*- @ '* - $"n $e#"j"t ee"n untupen3eut "$"l"2

$4+- .+- n+'*- '* - @,


12/50

, >"t" "t" penol""n $"e#"2 #iti

7 -919 - &"" 78+ -919+ ( %un""n

t"el F untu 7 -919+),

D"#i t"el untu 7 -919+1 $4 -*(pe&il"n% ) - .*- $"n $4 + (pen3eut ) -@ e2in%%" "t" #itin3" "$"l"2 F 9,9+1 1 @-

B1 C,

, Atu#"n eputu"n

Tol" H9 $"n te#i&" H* ji" RU46 B,C ji"

ti$" $e&ii"n te#i&" H9


13/50

, R"io Uji

@, Pen%"&il"n Keputu"n

K"#en" RUF5 B1C &"" H

o:

*

+

- ++ $ite#i&",

H"l ini e#"#ti ti$" te#$"p"tpe#e$""n 3"n% i%ni;"nte#2"$"p ."#i"el 2"il te#2"$"pe$u" epe#i&en te#eut,

656,298

29,262

2

2

1 ===

s

s

RU


14/50

Se"n$"in3" 2"n3" $iin%in"n &el"u"n uji "tu ujun%&"" 2ipotei "lte#n"ti4n3" &enj"$i :

Hipotei H* : *+

6 ++

>"t" $"e#"2 penol""n #iti "tu ujun% :

Di%un""n 7 -919 - &"" 7 -919 ( %un""n

t"le F untu 7 -919+ $4* pe&il"n% - .*- $"n $4+(pen3eut ) - @ e2in%%" "t" #itin3" "$"l"2

F9,9+1 1 @ - C,9,

Atu#"n pen%"&il"n eputu"n

Tol" H9 $"n te#i&" H* ji" RU46 C,9 ji" ti$"

$e&ii"n te#i&" H9,

Pen%"&il"n eputu"n,

K"#en" RUF5 C,9 &"" Ho : *+- ++ $ite#i&" ,


15/50


16/50

Uji Hipotesis Mean dengan Sampel Ganda

D"l"& uji 2ipotei &e"n $en%"n "&pel %"n$"1 "u&i"2?" e$u" $it#iui no#&"l tet"p $i%un""n1 n"&un$e&ii"n p#oe$u# uji 2ipotein3" $"p"t &en%iuti t"2"p"n3"n% e#e$" 3"n% te#%"ntun% p"$" on$ii "&peln3",

Se0"#" u&u& "$" B p#oe$u# uji 3"itu :

Uji tp""n%"n untu popul"i te#%"ntun% ( dependentpopulation ),

Uji untu popul"i 3"n% in$epen$ent $"n ji" ."#i"nipopul"i $iet"2ui "t"u ji" e$u" "&pel uu#"nn3"

$iet"2uiUji t "&pel uu#"n e0il untu popul"i 3"n% "lin%e" (independent) ji" uji F'n3" &enunju"n /*+/++

Uji t "&pel uu#"n e0il ji" popul"i 3"n% "lin% e"(independent) ji" uji F'n3" $iet"2ui /*+- /++,


17/50

Uji t pasangan untuk populasi salingtergantung

Prosedur:Pe#n3"t""n Hipotei nol $"n Hipotei Alte#n"ti4

D"l"& uji ini 2ipotei noln3" "$"l"2 pe#e$""n#"t"'#"t"n3" "$"l"2 nol, Se$"n%"n 2ipotei

"lte#n"ti4n3" "$"l"2 te#$"p"t pe#e$""n nil"i#"t"'#"t",

H9 : $- 9

H* : $ 9 uji $u" ujun% ( $6 9 uji "tu ujun% )

Pe&ili2"n tin%"t epentin%"n (level ofsignicance)1 7


18/50

Penentu"n $it#iui pen%uji"n 3"n%$i%un""n

Seu"i n"&"n3" &"" $it#iui ini3"n% $i%un""n "$"l"2 $it#iui t,

Pen$e;nii"n $"e#"2 penol""n "t"u

$"e#"2 #iti,D"l"& &en%%un""n $it#iui tuntu

pen%uji"n ini $e#"j"t ee""n $4$itentu"n $en%"n #u&u $4 - . - n '*1

$en%"n n"$"l"2 "n3"n3" p""n%"n$"t",

Pe#n3"t""n "tu#"n eputu"n (DecissionRule),


19/50

Ru&u 3"n% $i%un""n untu&en%2itun% #"io uji "$"l"2 :

$en%"n d"$"l"2 pe#e$""n nil"ip""n%"n $"t" eelu& $"n eu$"2$ipe#l"u"n

Pen%"&il"n eputu"n e0"#" t"titi :

Ji" #"io uji e#"$" $i $"e#"2 pene#i&""n&"" 2ipotei nol $ite#i&" $"n ji"e#"$" $i $"e#"2 penol""n &""

2ipotei nol $itol",

1

)(

/

1

2

=

==

=

n

dd

s

ns

dtRU

n

i

d

d

d

test


20/50

=onto2

Seo#"n% inin3u# ""n&en%e."lu"i p#o%#"& "#u untu&enj"l"n"n eu"2 p#oe$u#pen%elol""n "i $"t" ( data base),

Ji" $"l"& p#o%#"& "#u te#eutte#$"p"t pen%2e&"t"n ?"tu $"#i

p"$" p#o%#"& ""t ini &"" i" ""n&e#eo&en$"i"n pe#u"2""nte#eut $en%"n p#o%#"& "#u,


21/50

Su"tu "&pel 3"n% te#$i#i $"#i @ ope#"to#$i"&il $"n e&u$i"n $"l"& ?"tu j"&

untu &en3ele"i"n pen%ol"2"n $"t"$i0"t"t,

Ke$el"p"n ope#"to# 3"n% "&" $il"ti2

&en%%un""n p#o%#"& 3"n% "#u "&p"i&"2i#,

Ke&u$i"n ?"tu 3"n% $ipe#lu"n untu

&en3ele"i"n pee#j""n 3"n% "&"$i0"t"t1 epe#ti 3"n% $itunju"n p"$"t"el1 e&u$i"n $il"u"n pe#2itun%"ne"%"i e#iut :


22/50


23/50

Uji 2ipotei $il"u"n $en%"n l"n%"2 e"%"i e#iut :

Hipotei

H9 : $- 9

H* : $ 9 uji $u" ujun%

Tin%"t epentin%"n 7 - 9,9 -

Men%%un""n $it#iui t

>"t"'"t" $"e#"2 penol""n "t"u $e#"2 #iti uji $u"

ujun%Di%un""n 7 - 919 - &"" 7 - 919 ( %un""n

t"le F untu 7 - 919+) $en%"n $4* (pe&il"n% ) -.*- $"n $4+ (pen3eut ) - @ "t" #itin3" "$"l"2 F

9,9+1 1@- +,C,Atu#"n Keputu"n

Tol" H9 $"n te#i&" H*ji" RUt 5 '+,C "t"u

RUt 6 +,C1 ji" ti$" $e&ii"n te#i&" H9


24/50

R"io Uji

Pen%"&il"n eputu"n

K"#en" '+,C 5 RUt5 +,C &""

H9 : $- 9 $ite#i&",

H"l ini e#"#ti #"t"'#"t" e0ep"t"n pen%elol""np#o%#"& "#u ti$" e#e$" $en%"n p#o%"&l"&",

J"$i inin3u# te#eut i"&e#eo&en$"i"n untu ti$" &en%%un""np#o%#"& "#u ep"$" pe#u"2""n,

37,18/14,4

02

/=

=

==

ns

dtRU

d

d

test


25/50

H"il output SPSS(te#li2"t t2it - *1C $"n nil"i'p - 91+*B

6 919 e2in%%" H9 $ite#i&")


26/50


27/50

Uji z untuk populasi yang saling bebas(independent)

Su"tu uji $i%un""n il" :

S"&pel 3"n% $i"&il $"#i e$u" popul"i 3"n% "lin% e" $"ne#$it#iui no#&"l,

Nil"i nil"i t"n$"#t popul"i /*$"n /+tel"2 $iet"2ui "t"u uu#"n

e$u" "&pel lei2 $"#i C9 ( n6 C9),

P#oe$u# uji 2ipotein3" e"%"i e#iut :Pe#n3"t""n 2ipotei nol $"n 2ipotei "lte#n"ti4D"l"& uji 2ipotei nol $"n 2ipotei "lte#n"ti4n3" "$"l"2 :

H9 : *- +

H* : * + uji $u" ujun%

( * 5 + uji "tu ujun% *6 + )

Pe&ili2"n tin%"t epentin%"n 7

Penentu"n $it#iui 3"n% $i%un""n,Seu"i $en%"n n"&"n3" $it#iui 3"n% $i%un""n "$"l"2

$it#iui


28/50

Pen$e;nii"n $e#"2 $e#"2penol""n "t"u $"e#"2 #iti,

Pe#n3"t""n "tu#"n eputu"n,Pe#2itun%"n #"io uji "$"l"2 :

Ru&u 3"n% $i%un""n untu #"io

uji "$"l"2 :Ji" /*$"n /+tel"2 $iet"2ui1

Pen%"&il"n eputu"n e0"#" t"titi,

2

2

1

1

21

nn

xxzRUtest

+

==


29/50

=onto2

Seu"2 pe#u"2""n teleo&uni"i e#%e#"&e&utu"n untu &e&""n% ite& "nten"jeni "#u $i t"iun #el"in3" untu&enin%"t"n ine#j" pe&i0"#""n $en%"npel"n%%"nn3",

Du" 0onto2 "ntenn" $"#i + pe&"o 0uup&e&"$"i untu pene#"p"n 3"n% $iin%in"n,Untu &enj"&in pe&"o"n $"n uu 0"$"n%

pe#u"2""n te#eut &e&utu"n untu&e&eli $"#i + pe&"o te#eut,

Den%"n 3"#"t ti$" "$" pe#e$""n "#tin3" $"3"

t"2"n ui" &e&ilii u&u# 3"n% "&",


30/50

Su"tu "&pel "0" $"#i C $"#i ite&"ntenn" pe#t"&" $"n C+ "nten" $"#i

pe&"o > ""n $iuji, R"t"'#"t" e%"%"l"n

$"#i ite& "ntenn" "$"l"2 +@99 2"#i $"#i"nten" A $"n +9 $"#i "ntenn" >,

Su"tu u&e# $"#i in$ut#i independent3"n% l"3" &en%i$enti;"i"n "2?"t"n$"#t $e.i"i untu ite& A "$"l"2 +99j"& $"n untu "ntenn" > "$"l"2 *@9 2"#i,

Den%"n tin%"t epentin%"n 919 &"""p""2 te#$"p"t pe#e$""n $"l"& ite&

"nten" te#eut


31/50

Uji 2ipotei $il"u"n $en%"n l"n%"2 e"%"ie#iut :

HipoteiH9 : *- +

H* : * + uji $u" ujun%

Tin%"t epentin%"n 7 - 9,9

Men%%un""n $it#iui

>"t" "t" $"e#"2 penol""n 8 "t" #iti$u" ujun% "$"l"2 7 - 9,9 e#"#ti 78+ -9,9+ $"#i t"el $i$"p"t"n nil"i #itie"%"i e#iut : *,

Atu#"n eputu"n

Tol" H9 $"n te#i&" H* ji" RU 5 *, "t"u

RU 5 '*,1 ji" ti$" $e&ii"n te#i&" H9


32/50

R"io uji

Pen%"&il"n eputu"nK"#en" '*,5 RU 5 *, &""H9 $ite#i&",

H"l ini "&" "#tin3" "2?" ti$""$" pe#e$""n "nt"#" ite&"ntenn" * $"n "ntenn" +,

08,143,46

27502800

43,46

36

180

35

200

2

2

2

1

2

1

21

22

2

2

2

1

2

1

=

=

+

=

=+=+

nn

xxRU

nn

=onto2


33/50

=onto2

H"il output SPSS


34/50

H"il output SPSS(te#li2"t nil"i'p 6 919 e2in%%" H9$ite#i&" 3"itu #"t"'#"t" e$u" el"

"&"


35/50

Uji l k k il k


36/50

Uji t sampel ukuran kecil untukpopulasi yang saling bebas jika uji!nyamenunjukkan "#

$% "$$

Uji ini ""n $i%un""n il" :

S"&pel $"#i e$u" popul"i

e#$it#iui no#&"lNil"i t"n$"#t popul"i /*$"n /+

ti$" $iet"2ui

Uu#"n n*$"n n+e0ilUji F p"$" ."#i"ni &enunju"n /*

+

/++


37/50

P#oe$u# pen%uji"nn3" &e#up""np#oe$u# pen%uji"n $u" ."#i"ni

$"n uji t $en%"n etentu"ne"%"i e#iut :

R"io uji

De#"j"t ee""n De#"j"t eee"n "$"l"2$e#"j"t 3"n% lei2 e0il $"#i $u""&pel te#eut,

2

2

2

1

2

1

21

n

s

n

s

xxRU

+

=


38/50

=onto2

A%en pen3e?""n %enet &en3"t""np"$" eu"2 pe#u"2""n 3"n% ""n&en3e?" eju&l"2 %enet "2"?" #"t"'#"t" i"3" %enet e#$"3" *9 ?2

"&"'"&" $i eto# A $"n > $i ot"te#eut,

Untu &en%uji pe#n3"t""n te#eut

&"" pe#u"2""n te#eut &en%"&il"&pel $i ee#"p" pe#e?""n %enet$i eto# A $"n eto# > $i ot"te#eut,


39/50

Di eto# A $en%"n *9 $"t"$ipe#ole2 #"t" #"t" eu"2 e?"

%enet "$"l"2 Rp ,9991' $en%"n$e.i"i Rp +,9991' $"n $i eto# >*+ $"t" $en%"n #"t"'#"t" e?" pe#

%enet "$"l"2 Rp @9,9991' $"n$e.i"i Rp C+,9991', "p""2 3"n%$"p"t $ii&pul"n $"#i $"t" $i "t"

$"n $en%"n tin%"t epentin%"n9,9


40/50

Uji 2ipotei ""n $il"u"n $en%"n l"n%"2e"%"i e#iut ini :

Uji atas &ariansi :

Hipotei :

Ho : /*+- /++

H*: /*+

/++

Tin%"t epentin%"n 7-9,9,

K"#en" ."#i"ni A lei2 e"# $"#i p"$" "&pel > &""."#i"ni untu n*- nA -*9 $"n n+ - n> - *+ &""$e#"j"t eee""nn3" "$"l"2 $4*- .*- n*'* -

e$"n%"n untu $4+ -.+-n+'*- **,

>"t" "t" $"e#"2 #iti untu penol""n "$"l"2 7 -9,9 &"" 78+ - 9,9+ $"#i t"le F untu 7 - 9,9+$"n $4* pe&il"n% - .* - $"n $4+ pen3eut- .+ -

**


41/50

Atu#"n eputu"n

Tol" H9 $"n te#i&" H* ji" RUF 6

C,C $"n ji" ti$" $e&ii"n te#i&"H9

R"io uji

Pen%"&il"n eputu"nK"#en" RUF 6 C, &"" H9 $i tol"

$en%"n "&" "#tin3" H*: /*+/++

$ite#i&",

745,332000

620002

2

2

2

21

====

s

sFRU

test


42/50

Uji t

Hipotei

H9 : *- +H* : * +

Tin%"t epentin%"n 7 - 9,9


>"t" "t" $"e#"2 #iti untupenol""n "$"l"2 7 - 9,9 &"" 78+

- 9,9+ $"#i t"el F untu 7 - 9,9+$"n $4* pe&il"n% - .* - $"n $4+pen3eut- .+ - ** $i$"p"t"n

"t" #itin3" - +,++,


43/50

Atu#"n eputu"n,

Tol" Ho $"n te#i&" H* ji RUt 5 '+,+

"t"u RUt 6+,+ ji" ti$" te#i&" H9,

R"io uji

Pen%"&il"n eputu"n

K"#en" ' +,++ 5 RUt 5 +,++ &""

H9 $ite#i&" 3"n% "&" "#tin3" $en%"nl"i& 3"n% $in3"t""n "%en %enette#eut en"#,

692,0

12

32000

10

62000

58000595000

22

2

2

2

1

2

1

21=

+

=

+

=

n

s

n

s

xxRU

t

Uji t sample dengan ukuran


44/50

Uji tsample dengan ukuranukuran kecil untuk populasi yangindependent dengan uji tela'

ditentukan "$# "$$Uji ini ""n $il"u"n il" :

S"&pel $"#i e$u" popul"i

e#$it#iui no#&"lNil"i t"n$"#t popul"i /*$"n /+

ti$" $iet"2ui

Uu#"n n*$"n n+ e0il (5 C9),Uji F p"$" ."#i"ni &enunju"n /+*

- /++


45/50

=onto2


46/50

=onto2Den%"n &en%ul"n% p"$" =onto2 * $i &"n" uji F

p"$" ."#i"ni &enuju"n "2?" /+

*- /+

+ &""uji t untu &e"nn3" "$"l"2 e"%"i e#iut :

Hipotei

H9 : *- +

H* : * +Tin%"t epentin%"n 7 - 9,9


>"t"'"t" $"e#"2 penol""n "t"u $"e#"2 #iti

uji ujun% ujun% 7 - 9,9 &"" 78+ - 9,9+$e#"j"t ee""n $i$"p"t"n

$4 - n* n+ < + - *,

D"#i t"el &"" ""n $i$"p"t"n nil"i e"%"i

e#iut ini : +,*C*,


47/50


48/50

=onto2


49/50

H"il output SPSS (te#li2"t "2?" nil"i'p 6919 e2in%%" #"t"'#"t" e$u" el" "&")


50/50

*+,M-.-S,H

Uji Hipotesis Adi 2

Documents

Transcript of Uji Hipotesis Adi 2