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Pertemuan 25 Uji Kesamaan Proporsi

Pertemuan 25 Uji Kesamaan Proporsi. Matakuliah : I0134 – Metoda Statistika Tahun : 2005 Versi : Revisi. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa dapat menghasilkan uji khi-kuadrat untuk uji kesamaan proporsi.

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Pertemuan 25 Uji Kesamaan Proporsi

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

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

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

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

  5. 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

  6. 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).

  7. Test of Independence: Contingency Tables 1. Set up the null and alternative hypotheses. 2. Select a random sample and record the observed frequency, fij , for each cell of the contingency table. 3. Compute the expected frequency, eij , for each cell.

  8. 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).

  9. 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

  10. Contoh Soal : Finger Lakes Homes • Contingency Table (Independence) Test • Hypotheses H0: Price of the home is independent of the style of the home that is purchased Ha: 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

  11. Contoh Soal : Finger Lakes Homes • 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.

  12. Selamat Belajar Semoga Sukses.

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