Matakuliah
Tahun
Versi
: I0134 – Metoda Statistika
: 2005
: Revisi
Pertemuan 25
Uji Kesamaan Proporsi
1

Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu :
• Mahasiswa dapat menghasilkan uji khi-kuadrat untuk uji kesamaan proporsi.
2

Outline Materi
• Hasil pengamatan
• Statistik uji khi-kuadrat
• Pengambilan keputusan
3

Uji Proporsi
• Goodness of Fit Test: A Multinomial
Population
• Tests of Independence: Contingency
Tables
• Goodness of Fit Test: Poisson and
Normal Distributions
4

A Multinomial Population
1 . Set up the null and alternative hypotheses.
2. Select a random sample and record the observed frequency, f i
, for each of the k categories.
3. Assuming H
0 is true, compute the expected frequency, e i
, in each category by multiplying the category probability by the sample size.
continued
5

A Multinomial Population
4. Compute the value of the test statistic.
 2 k k i i

1
( ( f f i i
 e i i
) ) e i i
5. Reject H
0 if
 
(where
 is the significance level and there are k - 1 degrees of freedom).
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Test of Independence: Contingency
Tables
1. Set up the null and alternative hypotheses.
2. Select a random sample and record the observed frequency, f table.
ij
, for each cell of the contingency
3. Compute the expected frequency, e ij cell.
, for each e ij

Sample Size j
7

Test of Independence:
Contingency Tables
4. Compute the test statistic.
 2   i
 j
( f ij
 e ij
)
2 e ij
5. Reject H
0
 2   2 if (where
 is the significance level and with n rows and m columns there are
( n - 1)( m - 1) degrees of freedom).
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Contoh Soal : Finger Lakes
Homes (B)
• Contingency Table (Independence) Test
Price Colonial Ranch Split-Level A-Frame
< $65,000 18 6 19 12
> $65,000 12 14 16 3
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
Contingency Table (Independence) Test
• Hypotheses
H
0
: Price of the home is independent of the style of the home that is purchased
H a
: Price of the home is not independent of the style of the home that is purchased
• Expected Frequencies
Price Colonial Ranch Split-Level A-Frame Total
< $99K 18 6 19 12 55
> $99K 12 14 16 3 45
Total 30 20 35 15 100
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Contoh Soal : Finger Lakes Homes
• Contingency Table (Independence) Test
– Test Statistic
 2 
( . )
2

(
11
)
2
 
( .
)
2
= .1364 + 2.2727 + . . . + 2.0833 = 9.1486
– Rejection Rule
With

= .05 and (2 - 1)(4 - 1) = 3 d.f.,
Reject H
0
– Conclusion if

2 > 7.81
 2
.
05

We reject H
0
, the assumption that the price of the home is independent of the style of the home that is purchased.
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• Selamat Belajar Semoga Sukses.
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