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

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

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

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

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

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).

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.

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).

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

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

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.

Selamat Belajar Semoga Sukses.