Matakuliah Tahun : L0104 / Statistika Psikologi : 2008 Pengujian Hipotesis Nilai Tengah Pertemuan 15 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menyusun simpulan dari langkah-langkah uji hipotesis nilai tengah dan beda nilai tengah. 3 Bina Nusantara Outline Materi • • • • Uji nilai tengah sampel besar Uji nilai tengah sampel kecil Uji beda nilai tengah dua populasi bebas Uji beda dua nilai tengah populasi tidak bebas 4 Bina Nusantara Hypothesis Testing • Developing Null and Alternative Hypotheses • Type I and Type II Errors • One-Tailed Tests About a Population Mean: Large-Sample Case • Two-Tailed Tests About a Population Mean: Large-Sample Case • Tests About a Population Mean: Small-Sample Case continued Bina Nusantara Developing Null and Alternative Hypotheses • Hypothesis testing can be used to determine whether a statement about the value of a population parameter should or should not be rejected. • The null hypothesis, denoted by H0 , is a tentative assumption about a population parameter. • The alternative hypothesis, denoted by Ha, is the opposite of what is stated in the null hypothesis. • Hypothesis testing is similar to a criminal trial. The hypotheses are: H0: The defendant is innocent Ha: The defendant is guilty Bina Nusantara Developing Null and Alternative Hypotheses • Testing Research Hypotheses – The research hypothesis should be expressed as the alternative hypothesis. – The conclusion that the research hypothesis is true comes from sample data that contradict the null hypothesis. Bina Nusantara A Summary of Forms for Null and Alternative Hypotheses about a Population Mean • The equality part of the hypotheses always appears in the null hypothesis. • In general, a hypothesis test about the value of a population mean μ must take one of the following three forms (where μ0 is the hypothesized value of the population mean). H0: μ > μ0 Ha: μ < μ0 Bina Nusantara H0: μ < μ0 Ha: μ > μ0 H0: μ = μ0 Ha: μ ≠ μ0 Contoh Soal: Metro EMS • Type I and Type II Errors Conclusion Accept H0 (Conclude μ <12) Reject H0 (Conclude μ > 12) Conclusion Bina Nusantara Population Condition H0 True Ha True (μ < 12 ) (μ > 12 ) Correct Conclusion Type II Error Type I Correct Error The Steps of Hypothesis Testing Bina Nusantara Determine the appropriate hypotheses. Select the test statistic for deciding whether or not to reject the null hypothesis. Specify the level of significance for the test. Use to develop the rule for rejecting H0. Collect the sample data and compute the value of the test statistic. a) Compare the test statistic to the critical value(s) in the rejection rule, or b) Compute the p-value based on the test statistic and compare it to to determine whether or not to reject H0. One-Tailed Tests about a Population Mean: Large-Sample Case (n > 30) Hypotheses H0: Ha: H0: Ha: Test Statistic Known x 0 z / n or Unknown x 0 z s/ n Rejection Rule Reject H0 if z > zReject H0 if z < -z Bina Nusantara Two-Tailed Tests about a Population Mean: Large-Sample Case (n > 30) • Hypotheses H0: μ = Ha: μ≠ • Test Statistic σ z μ0 Known x 0 / n μ σ Unknown x 0 z s/ n • Rejection Rule Reject H0 if |z| > z Bina Nusantara Tests about a Population Mean: Small-Sample Case (n < 30) • Test Statistic σ Known σ Unknown x 0 x 0 t t / n s/ n This test statistic has a t distribution with n - 1 degrees of freedom. • Rejection Rule One-Tailed Two-Tailed H0: μ <μ0 Reject H0 if t > tα H0: μ> μ0 Reject H0 if t < -tα H0: μ = μ0 Bina Nusantara Reject H0 if |t| > t 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 Ha: p < p0 Bina Nusantara H0: p < p0 Ha: p > p0 H0: p = p0 Ha: p ≠ p0 Hypothesis Tests About the Difference Between the Means of Two Populations: Independent Samples • Hypotheses H0: μ1 - μ2 < 0 Ha: μ1 - μ2 > 0 H0: μ1 - μ2 > 0 Ha: μ1 - μ2 < 0 H0: μ1 - μ2 = 0 Ha: μ1 - μ2 ≠ 0 • Test Statistic Large-Sample z Bina Nusantara ( x1 x2 ) ( 1 2 ) 12 n1 22 n2 Small-Sample t ( x1 x2 ) ( 1 2 ) s2 (1 n1 1 n2 ) Contoh Soal: Specific Motors • Hypothesis Tests About the Difference Between the Means of Two Populations: Small-Sample Case – Rejection Rule Reject H0 if t > 1.734 (a = .05, d.f. = 18) – Test Statistic t s2 (1 n1 1 n2 ) (n1 1)s12 (n2 1)s22 where: s n1 n2 2 2 Bina Nusantara ( x1 x2 ) ( 1 2 ) Contoh Soal: Express Deliveries District Office Seattle Los Angeles Boston Cleveland New York Houston Atlanta St. Louis Milwaukee Denver Bina Nusantara Delivery Time (Hours) UPX INTEX Difference 32 25 7 30 24 6 19 15 4 16 15 1 15 13 2 18 15 3 14 15 -1 10 8 2 7 9 -2 16 11 5 Contoh Soal: Express Deliveries • Inference About the Difference Between the Means of Two Populations: Matched Samples di ( 7 6... 5) d 2. 7 n 10 2 76.1 ( di d ) sd 2. 9 n 1 9 d d 2. 7 0 t 2. 94 sd n 2. 9 10 – Conclusion Reject H0. There is a significant difference between the mean delivery times for the two services. Bina Nusantara Selamat Belajar Semoga Sukses Bina Nusantara
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