Matakuliah
: I0014 / Biostatistika
Tahun
: 2008
Pengujian Hipotesis (II)
Pertemuan 12
Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
• Mahasiswa dapat menguji hipotesis untuk proporsi
(C3)
• Mahasiswa dapat menguji hipotesis untuk ragam
tengah (C3)
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Outline Materi
• Pendugaan Proporsi
• Pendugaan Ragam
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Pengujian Proporsi Populasi
When the sample size is large (both np> 5 and nq >
5),
the distribution of the sample proportion may be
approximated
Large - sample test statistic for the population proportion, p:
by a normal distribution with mean p and variance pq.
p  p0
z
p0 q 0
n
where q 0  (1  p0 )
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Pengujian Ragam Populasi
1. Rumuskan hipotesis nol :
H 0 :  2   02
H 0 :  2   02
H 0 :  2   02
2. Rumuskan hipotesisi alternatif:
H1 :  2   0 2
H1 :  2   0 2
H1 :  2   0 2
α
3. Tentukan taraf nyata uji:
 hit
4. Tentukan nilai hitung uji statistik:
2
Bina Nusantara

n  1S

0
2
2
5. Tentukan wilayah
kritis:
 2 hit   21 untuk H1 :  2   0 2
 2 hit   2
untuk H1 :  2   0 2
 2 hit   21
dan  2 hit   2 untuk H1 :  2   0 2
2
2
 2 ,  21 ,  2 2 ,  21 2
merupakan nilai khi kuadrat dengan db = v = n-1
6. Kesimpulan: tolak H0 bila 2hit jatuh di wilayah kritis
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Uji Dua Proporsi Populasi
•
Hypothesized difference is zero
– I: Difference between two population proportions is 0
• p 1 = p2
» H0: p1 -p2 = 0
» H1: p1 -p20
– II: Difference between two population proportions is less than 0
• p1 p2
» H0: p1 -p2  0
» H1: p1 -p2 > 0
•
Hypothesized difference is other than zero:
– III: Difference between two population proportions is less than D
• p1 p2+D
» H0:p-p2  D
» H1: p1 -p2 > D
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Dihipotesiskan Beda Dua Proporsi
Nol
When the population proportions are hypothesized to be equal, then a pooled estimator of
the proportion (
) pmay be used in calculating the test statistic.
A large-sample test statistic for the difference between two population
proportions, when the hypothesized difference is zero:
z
( p1  p 2 )  0
1 1
p(1  p)  
 n1 n2 
x1
x
is the sample proportion in sample 1 and p 1  1 is the sample
n1
n1
proportion in sample 2. The symbol p stands for the combined sample
where p1 
proportion in both samples, considered as a single sample. That is:
p 
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x1  x1
n1  n 2
Uji Kesamaan Ragam Dua
Populasi
Test statistic for the equality of the variances of two normally
distributed populations:
F n 1,n 1
1
2
•
I: Two-Tailed Test
•
1 = 2
• H0: 1 = 2
• H1: 2
II: One-Tailed Test
• 12
• H0: 1  2
• H1: 1  2
•
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s12
 2
s2
Penutup
• Sampai saat ini Anda telah mempelajari
pengujian hipotesis untuk ragam, dan
proporsi, baik satu populasi maupun dua
populasi
• Untuk dapat lebih memahami penggunaan
pengujian hipotesis tersebut, cobalah Anda
pelajari materi penunjang, dan mengerjakan
latihan
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