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Pertemuan 25Uji Kesamaan Proporsi

Matakuliah : I0134 – Metoda Statistika

Tahun : 2005

Versi : Revisi

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Learning Outcomes

Pada akhir pertemuan ini, diharapkan mahasiswa

akan mampu :

• Mahasiswa dapat menghasilkan uji khi-kuadrat untuk uji kesamaan proporsi.

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Outline Materi

• Hasil pengamatan

• Statistik uji khi-kuadrat

• Pengambilan keputusan

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Uji Proporsi

• Goodness of Fit Test: A Multinomial Population

• Tests of Independence: Contingency Tables

• Goodness of Fit Test: Poisson and Normal Distributions

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A Multinomial Population

1. Set up the null and alternative hypotheses.

2. Select a random sample and record the observed

frequency, fi , for each of the k categories.

3. Assuming H0 is true, compute the expected frequency, ei , in each category by multiplying the category probability by the sample size.

continued

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A Multinomial Population

4. Compute the value of the test statistic.

5. Reject H0 if

(where is the significance level and there are k - 1 degrees of freedom).

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1

( )f ee

i i

ii

k2

2

1

( )f ee

i i

ii

k

2 2 2 2

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Test of Independence: Contingency Test of Independence: Contingency TablesTables

1. 1. Set up the null and alternative Set up the null and alternative hypotheses.hypotheses.

2. Select a random sample and record 2. Select a random sample and record the observedthe observed

frequency, frequency, ffij ij , for each cell of the , for each cell of the contingency table.contingency table.

3. Compute the expected frequency, 3. Compute the expected frequency, eeij ij , , for each cell. for each cell. e

i jij

(Row Total )(Column Total ) Sample Size

ei j

ij (Row Total )(Column Total )

Sample Size

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Test of Independence: Contingency Tables

4. Compute the test statistic.

5. Reject H0 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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( )f e

eij ij

ijji2

2

( )f e

eij ij

ijji

2 2 2 2

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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) TestContingency Table (Independence) Test

• HypothesesHypotheses

HH00: Price of the home : Price of the home isis independent of independent of the style the style of the home that is purchased of the home that is purchased

HHaa: Price of the home : Price of the home is notis not independent of theindependent of the

style of the home that is purchasedstyle of the home that is purchased

• Expected FrequenciesExpected Frequencies

PricePrice Colonial Ranch Split-Level A-Frame Colonial Ranch Split-Level A-Frame Total Total

<< $99K 18 $99K 18 6 19 12 6 19 12 55 55

> $99K 12 14 16 > $99K 12 14 16 3 45 3 45

Total 30 20 35 Total 30 20 35 15 10015 100

Contoh Soal : Finger Lakes Contoh Soal : Finger Lakes HomesHomes

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• Contingency Table (Independence) Test– Test Statistic

= .1364 + 2.2727 + . . . + 2.0833 = 9.1486– Rejection Rule

With = .05 and (2 - 1)(4 - 1) = 3 d.f.,

Reject H0 if 2 > 7.81

– Conclusion

We reject H0, the assumption that the price of the home is independent of the style of the home

that is purchased.

22 2 218 16 5

16 56 11

113 6 75

6 75 ( . )

.( )

. .( . )

. . 2

2 2 218 16 516 5

6 1111

3 6 756 75

( . ).

( ). .

( . ).

.

. .052 7 81. .052 7 81

Contoh Soal : Finger Lakes Homes

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• Selamat Belajar Semoga Sukses.