2. Pengujian Hipotesis Nilai Tengah Pertemuan 15 Matakuliah: L0104 / Statistika Psikologi Tahun : 2008

3. Bina Nusantara Learning Outcomes 3 Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menyusun simpulan dari langkah-langkah uji hipotesis nilai tengah dan beda nilai tengah.

4. Bina Nusantara Outline Materi 4 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

5. 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

6. 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 H 0, is a tentative assumption about a population parameter. The alternative hypothesis, denoted by H a, is the opposite of what is stated in the null hypothesis. Hypothesis testing is similar to a criminal trial. The hypotheses are: H 0 : The defendant is innocent H a : The defendant is guilty

7. Bina Nusantara 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. Developing Null and Alternative Hypotheses

8. 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 μ 0 is the hypothesized value of the population mean). H 0 : μ > μ 0 H 0 : μ < μ 0 H 0 : μ = μ 0 H a : μ μ 0 H a : μ ≠ μ 0

9. Bina Nusantara Type I and Type II Errors Population Condition H 0 True H a True Conclusion (μ 12 ) Accept H 0 Correct Type II (Conclude μ  <12) Conclusion Error Reject H 0 Type I Correct (Conclude μ > 12)  Error Conclusion Contoh Soal: Metro EMS

10. Bina Nusantara The Steps of Hypothesis Testing n Determine the appropriate hypotheses. n Select the test statistic for deciding whether or not to reject the null hypothesis. Specify the level of significance  for the test. Specify the level of significance  for the test. Use  to develop the rule for rejecting H 0. Use  to develop the rule for rejecting H 0. n Collect the sample data and compute the value of the test statistic. n 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 H 0.

11. Bina Nusantara n Hypotheses H 0 :   or H 0 :   H a :   H a :   n Test Statistic  Known  Unknown  Known  Unknown n Rejection Rule Reject H 0 if z > z  Reject H 0 if z z  Reject H 0 if z < - z  One-Tailed Tests about a Population Mean: Large-Sample Case ( n > 30)

12. Bina Nusantara HypothesesH 0 : μ  =  μ 0  H a :  μ ≠  μ  Test Statistic σ  Known σ Unknown Rejection Rule Reject H 0 if |z| > z  Two-Tailed Tests about a Population Mean: Large-Sample Case (n > 30)

13. Bina Nusantara Test Statisticσ  Knownσ Unknown This test statistic has a t distribution with n - 1 degrees of freedom. Rejection Rule One-Tailed Two-Tailed H 0 : μ  t α H 0 : μ>  μ 0 Reject H 0 if t < -t α H 0 : μ  =  μ 0 Reject H 0 if |t| > t  Tests about a Population Mean: Small-Sample Case (n < 30)

14. Bina Nusantara 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

15. Bina Nusantara Hypothesis Tests About the Difference Between the Means of Two Populations: Independent Samples Hypotheses H 0 : μ 1 - μ 2 0 H 0 : μ 1 - μ 2 = 0 H a : μ 1 - μ 2 > 0 H a : μ 1 - μ 2 < 0 H a : μ 1 - μ 2 ≠ 0 Test Statistic Large-Sample Small-Sample

16. Bina Nusantara 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 where:

17. Bina Nusantara Delivery Time (Hours) District OfficeUPX INTEX Difference Seattle 32 25 7 Los Angeles 30 24 6 Boston 19 15 4 Cleveland 16 15 1 New York 15 13 2 Houston 18 15 3 Atlanta 14 15 -1 St. Louis 10 8 2 Milwaukee 7 9 -2 Denver 16 11 5 Contoh Soal: Express Deliveries

18. Bina Nusantara Inference About the Difference Between the Means of Two Populations: Matched Samples –Conclusion Reject H 0. There is a significant difference between the mean delivery times for the two services. Contoh Soal: Express Deliveries

19. Bina Nusantara Selamat Belajar Semoga Sukses