Pertemuan 09 Pengujian Hipotesis 2 Matakuliah : I0262 – Statistik Probabilitas Tahun : 2007 Versi : Revisi Pertemuan 09 Pengujian Hipotesis 2

Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat memilih statistik uji proporsi, ragam dan uji kebaikan suai.

Uji hipotesis proporsi Uji hipotesis ragam Uji kebaikan suai Outline Materi Uji hipotesis proporsi Uji hipotesis ragam Uji kebaikan suai

H0: p > p0 H0: p < p0 H0: p = p0 A Summary of Forms for Null and Alternative Hypotheses about a Population Proportion The equality part of the hypotheses always appears in the null hypothesis. In general, a hypothesis test about the value of a population proportion p must take one of the following three forms (where p0 is the hypothesized value of the population proportion). H0: p > p0 H0: p < p0 H0: p = p0 Ha: p < p0 Ha: p > p0 Ha: p p0

Tests about a Population Proportion: Large-Sample Case (np > 5 and n(1 - p) > 5) Test Statistic where: Rejection Rule One-Tailed Two-Tailed H0: pp Reject H0 if z > z H0: pp Reject H0 if z < -z H0: pp Reject H0 if |z| > z

Two-Tailed Test about a Population Proportion: Large n Example: NSC Two-Tailed Test about a Population Proportion: Large n Hypothesis H0: p = .5 Ha: p .5 Test Statistic

Contoh Soal: NSC Two-Tailed Test about a Population Proportion: Large n Rejection Rule Reject H0 if z < -1.96 or z > 1.96 Conclusion Do not reject H0. For z = 1.278, the p-value is .201. If we reject H0, we exceed the maximum allowed risk of committing a Type I error (p-value > .050).

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

Goodness of Fit Test: 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

Goodness of Fit Test: 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).

Contoh Soal: Finger Lakes Homes Multinomial Distribution Goodness of Fit Test The number of homes sold of each model for 100 sales over the past two years is shown below. Model Colonial Ranch Split-Level A-Frame # Sold 30 20 35 15

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