1 / 23

Pertemuan 16 Pengujian Hipotesis Proporsi dan Varians

Pertemuan 16 Pengujian Hipotesis Proporsi dan Varians. Matakuliah : I0284 - Statistika Tahun : 2005 Versi : Revisi. Learning Outcomes. Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat menyusun simpulan dari hasil uji hipotesis proporsi dan varians.

aquene
Télécharger la présentation

Pertemuan 16 Pengujian Hipotesis Proporsi dan Varians

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pertemuan 16Pengujian Hipotesis Proporsi dan Varians Matakuliah : I0284 - Statistika Tahun : 2005 Versi : Revisi

  2. Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : • Mahasiswa akan dapat menyusun simpulan dari hasil uji hipotesis proporsi dan varians.

  3. Outline Materi • Uji hipotesis proporsi sampel besar • Uji hipotesis beda proporsi sampel besar • Uji hipotesis varians • Uji hipotesis kesamaan dua varians

  4. 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

  5. Hypothesis Testing • Tests About a Population Proportion • Hypothesis Testing and Decision Making • Calculating the Probability of Type II Errors • Determining the Sample Size for a Hypothesis Test about a Population Mean

  6. 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

  7. 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.

  8. 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  must take one of the following three forms (where 0 is the hypothesized value of the population mean). H0: >0 H0: <0 H0:  = 0 Ha:  < 0 Ha:  > 0 Ha: 0

  9. Type I and Type II Errors • Since hypothesis tests are based on sample data, we must allow for the possibility of errors. • A Type I error is rejecting H0 when it is true. • A Type II error is accepting H0 when it is false. • The person conducting the hypothesis test specifies the maximum allowable probability of making a Type I error, denoted by  and called the level of significance. • Generally, we cannot control for the probability of making a Type II error, denoted by . • Statistician avoids the risk of making a Type II error by using “do not reject H0” and not “accept H0”.

  10. Contoh Soal: Metro EMS • Type I and Type II Errors Population Condition H0 True Ha True Conclusion ( ) ( ) Accept H0Correct Type II (Conclude  Conclusion Error RejectH0Type I Correct (Conclude  rror Conclusion

  11. The Use of p-Values • The p-value is the probability of obtaining a sample result that is at least as unlikely as what is observed. • The p-value can be used to make the decision in a hypothesis test by noting that: • if the p-value is less than the level of significance , the value of the test statistic is in the rejection region. • if the p-value is greater than or equal to , the value of the test statistic is not in the rejection region. • Reject H0 if the p-value < .

  12. The Steps of Hypothesis Testing • 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.

  13. One-Tailed Tests about a Population Mean: Large-Sample Case (n> 30) • Hypotheses • H0:   or H0:  Ha: Ha: • Test Statistic  Known Unknown • Rejection Rule Reject H0 if z > zReject H0 if z < -z

  14. Contoh Soal: Metro EMS • One-Tailed Test about a Population Mean: Large n Let  = P(Type I Error) = .05 Sampling distribution of (assuming H0 is true and  = 12) Reject H0 Do Not Reject H0  1.645 c 12 (Critical value)

  15. Contoh Soal: Metro EMS • One-Tailed Test about a Population Mean: Large n Let n = 40, = 13.25 minutes, s = 3.2 minutes (The sample standard deviation s can be used to estimate the population standard deviation .) Since 2.47 > 1.645, we reject H0. Conclusion: We are 95% confident that Metro EMS is not meeting the response goal of 12 minutes; appropriate action should be taken to improve service.

  16. Contoh Soal: Metro EMS • Using the p-value to Test the Hypothesis Recall that z = 2.47 for = 13.25. Then p-value = .0068. Since p-value < , that is .0068 < .05, we reject H0. Reject H0 Do Not Reject H0 p-value z 0 1.645 2.47

  17. Two-Tailed Tests about a Population Mean: Large-Sample Case (n> 30) • Hypotheses H0: =  Ha:  • Test Statistic  Known Unknown • Rejection Rule Reject H0 if |z| > z

  18. Summary of Test Statistics to be Used in aHypothesis Test about a Population Mean Yes No n > 30 ? No Popul. approx. normal ? s known ? Yes Yes Use s to estimate s No s known ? No Use s to estimate s Yes Increase n to > 30

  19. 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 pmust take one of the following three forms (where p0 is the hypothesized value of the population proportion). H0: p>p0H0: p<p0H0: p = p0 Ha: p < p0Ha: p > p0Ha: pp0

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

  21. Hypothesis TestingAbout a Population Variance • Right-Tailed Test • Hypotheses • Test Statistic • Rejection Rule Reject H0 if (where is based on a chi-square distribution with n - 1 d.f.) or Reject H0 if p-value < a

  22. Hypothesis TestingAbout a Population Variance • Two-Tailed Test • Hypotheses • Test Statistic • Rejection Rule Reject H0 if (where are based on a chi-square distribu- tion with n - 1 d.f.) or Reject H0 if p-value < a

  23. Selamat Belajar Semoga Sukses.

More Related