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7/25/2019 Pertemuan 06 Baru-Uji Hipotesis Satu Populasi.pptx
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Metode Statistika II
Pertemuan 6 - Uji Hipotesis Rata-
rata
Oleh : Rudi Salam
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Uji Hipotesis Rata-rata
Known
LargeSamples
Unknown
Hypothesis
Tests for
SmallSamples
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Known
LargeSamples
Unknown
HypothesisTests for
SmallSamples
"he test statistic is:
#alculatin$ the "est Statistic
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Known
LargeSamples
Unknown
HypothesisTests for
SmallSamples
"he test statistic is:
#alculatin$ the "est Statistic
&ut issometimes
appro'imatedusin$ a (:
(continued)
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Known
LargeSamples
Unknown
HypothesisTests for
SmallSamples
"he test statistic is:
#alculatin$ the "est Statistic
*"he population must+e appro'imatel,
normal
(continued)
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Re/ie0: Steps in H,pothesis"estin$
. Speci1, the population /alue o1 interest
!. 2ormulate the appropriate null andalternati/e h,potheses
%. Speci1, the desired le/el o1 si$ni3cance
). 4etermine the rejection re$ion
. O+tain sample e/idence and computethe test statistic
6. Reach a decision and interpret theresult
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H,pothesis "estin$ 5'ample
Test the claim that the true mean# of TV sets in US homes is at
least 3.!ssume " $.%&
1. Specify the population value of interest The mean number of TVs in US homes
2. Formulate the appropriate null an alternative
hypotheses
!"# $ !%# & $ 'This is a lo(er tail test) $. Specify the esire level of si*nificance
Suppose that + .", is chosen for this test
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Reject H7 4o not rejectH7
). 4etermine the rejection re$ion
8 .7
'() '*.+,- 7
"his is a one-tailed test 0ith 8 .7.Since " is known9 the cuto /alue is a ( /alue:
Reject H7i1 ( ; (8 -.6) < other0ise do not
reject H7
H,pothesis "estin$ 5'ample(continued)
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. O+tain sample e/idence and computethe test statistic
Suppose a sample is taken 0ith the 1ollo0in$
results: n 8 779 ' 8 !.=) *8 7.= is assumedkno0n
"hen the test statistic is:
H,pothesis "estin$ 5'ample
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.
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Reject H7 4o not rejectH7
8 .7
'*.+,- $
6. Reach a decision and interpret the result
'.$
Since ( 8 -!.7 ; -.6)9 0e reject the nullh,pothesis that the mean num+er o1 "?s inUS homes is at least %
H,pothesis "estin$ 5'ample(continued)
(
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Reject H7
8 .7
.%+%
,
4o not rejectH7 3
n alternate 0a, o1 constructin$ rejection re$ion:
.%,
Since ' 8 !.=) ;!.=6=)9 0e reject thenull h,pothesis
H,pothesis "estin$ 5'ample(continued)
/
Ao0e'pressed in '9not (units
rudisalam@stis.ac.id-
2.--/1""
".-1./,$
n
zx 00 ===
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p-?alue pproach to "estin$
#on/ert Sample Statistic *e.$. to"est Statistic *Z or t statistic
O+tain the p-/alue1rom a ta+le orcomputer
#ompare the p-/alue0ith
I1 p-/alue ; 9 reject H7
I1 p-/alue
9 do not reject H7
'
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p-?alue pproach to "estin$
p-/alue: Pro+a+ilit, o1 o+tainin$ a
test statistic more e'treme * B or
than the o+ser/ed sample /alue$i/en H7is true
lso called o+ser/ed le/el o1
si$ni3cance
Smallest /alue o1 1or 0hich H7can
+e rejected
(continued)
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p'0alue.$%
8 .7
p-/alue e'ample
5'ample: Ho0 likel, is it to see a samplemean o1 !.=) *or somethin$ 1urther +elo0the mean i1 the true mean is 8 %.7C
.%+%,
3
.%,
/
rudisalam@stis.ac.id-
."22-2.")'z
1""".-
$."2.-/
z
$.")2.-/x'
=
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#ompare the p-/alue 0ith
I1 p-/alue ; 9 reject H7 I1 p-/alue 9 do not reject
H7
Here: p-/alue 8 .7!!=
8 .7Since .$% 1 .$-2 wereect the nullhypothesis
(continued)p-/alue e'ample
p'0alue
.$%
8 .7
.%+%,
3
.%, rudisalam@stis.ac.id-
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5'ample: Upper "ail ( "est1or Mean *Dno0n
phone industr, mana$er thinks thatcustomer monthl, cell phone +ill ha/eincreased9 and no0 a/era$e o/er E!
per month. "he compan, 0ishes totest this claim. *ssume 8 7 iskno0n
H7: F B ! the a/era$e is not o/er E! permonth
H: F G ! the a/era$e is$reater than E! per
month
*i.e.9 sucient e/idence e'ists to support themana$ers claim
2orm h,pothesis test:
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Reject H74o not rejectH7
Suppose that 8 .7 is chosen 1or this test
2ind the rejection re$ion:
.*$
()*.
%7
4eect H$
Reject H7i1 ( G
.!=
5'ample: 2ind RejectionRe$ion
(continued)
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2indin$ #ritical ?alue - One"ail
Z .7 .7>
. .%>7.%=7 .%=%7
*..%>=7 .)7
.% .)).)6! .)z 7 *.%
.$%
Standard Aormal4istri+ution "a+le*Portion
Jhat is ( $i/en 87.7C
8 .7
5riticalValue
*.%
.6$
.%>>
.*$
.)7.7
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O+tain sample e/idence and compute thetest statistic
Suppose a sample is taken 0ith the1ollo0in$ results: n 8 6)9 ' 8 %. *87
0as assumed kno0n
"hen the test statistic is:
5'ample: "est Statistic(continued)
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Reject H7
.*$
4o not rejectH7 *.%
7
4eect H$
( .%%
#alculate the p-/alue and compare to
(continued)
p'0alue .*%6,
p -?alue Solution
7o not reect H$since p'0alue .*%6, 9
.*$
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.1-3/
.$1".,".--)'z
/1"
,2.",$.1z
,2."),$.1x'
===
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5'ample: "0o-"ail "est*Unkno0n
"he a/era$e cost o1 ahotel room in Ae0
Kork is said to +eE6= per ni$ht. random sample o1 !hotels resulted in '
8 E!.7 and
s 8 E.)7. "est atthe
8 7.7 le/el.
H$:
*+%
H!:
*+%
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8 $.$-
n
-
is unknown2so
use a tstatistic
5ritical Value:
t, ; .$+36
5'ample Solution: "0o-"ail
"est
7o not reect H$:not sucient e/idence
that true mean cost is dierent than E6=
Reject H7Reject H7
L!8.7!
-tL!4o not rejectH7 7
tL!
L!8.7!
'.$+36 .$+36*.,+
H$:
*+% H!:
*+%
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Uji Proporsi Satu Populasi
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Uji Hipotesis untuk Proporsi
Meli+atkan nilai kate$ori
4ua outcome ,an$ mun$kin
NSukses *memiliki karakteristik tertentu
Na$al *tidak memiliki karakteristik tertentuterse+ut
2raksi atau proporsi populasi dalamkate$ori NsuksesQ dinotasikan den$an p
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Proporsi
Proporsi sampel pada kate$ori suksesdin,atakan den$an p
Detika npdan n*-ppalin$ tidak +ernilai
9 pdapat diapproksimasi den$andistri+usi normal den$an rata-rata danstandar de/iasi
(continued)
number of successes in samplepsample size
xn= =
p p=
p
p(1 p)
n
=
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4istri+usisamplin$ dari padalah normal9
sehin$$astatistic ujin,aadalah ( :
Uji Hipotesis untuk Proporsi
np -an!8)67
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Z "est 1or Proportion:Solution
8 .7
n 8 779 p 8 .7
Reject H7at 8 .7
H$: p .
$% H!: p
.$%
5ritical Values: ;*.6+
Test Statistic:
7ecision:
5onclusion:
z$
4eect
4eect
.7!
.7!
*.6+
-!.)
"here is suciente/idence to rejectthe compan,s claim
o1 = response rate.
'*.6+
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2./4
,""
."-)."-'1
."-.",
n
p)p'1
ppz =
=
=
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4o not rejectH7 4eect H$4eect
H$ L!8 .7!
*.6+7
( '.,=
#alculate the p-/alue and compare to*2or a t0o sided test the p-/alue is al0a,s t0o sided
(continued)
p'0alue .
$*3+:
p -?alue Solution
4eect H$since p'0alue .$*3+ 1
.$-
( .,=
'*.6+
L!8 .7!
.$$+%
.$$+%
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"."1$2'.""-)
./3$2)2'.,
2./4)'x2./4)'z
==
=
+
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Soal
Se+uah uan$ lo$am dilantun !7 kali danmen$hasilkan muka. pakah dari sinicukup ada alasan untuk menolak hipotesis+ah0a uan$ tadi setan$kup dan me,akinitandin$ann,a +ah0a muka muncul kuran$dari 7C Se+utkan p-/alue n,a.
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#hapter Summar,
"erima Dasih
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