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Pengujian Hipotesis Nilai Tengah Pertemuan 15

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

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Pengujian Hipotesis Nilai Tengah Pertemuan 15

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  1. Pengujian Hipotesis Nilai TengahPertemuan 15 Matakuliah : L0104 / Statistika Psikologi Tahun : 2008

  2. 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

  3. 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

  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. 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

  6. 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.

  7. 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 H0: μ<μ0H0: μ = μ0 Ha: μ < μ0Ha: μ > μ0Ha: μ ≠ μ0

  8. Contoh Soal: Metro EMS • Type I and Type II Errors Population Condition H0 True Ha True Conclusion (μ < 12 ) (μ > 12 ) Accept H0Correct Type II (Conclude μ <12) Conclusion Error Reject H0Type I Correct (Conclude μ > 12) Error Conclusion

  9. 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.

  10. 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

  11. Two-Tailed Tests about a Population Mean: Large-Sample Case (n> 30) • Hypotheses H0: μ= μ0  Ha: μ≠ μ • Test Statistic σKnownσ Unknown • Rejection Rule Reject H0 if |z| > z

  12. Tests about a Population Mean:Small-Sample Case (n < 30) • Test Statistic σKnownσ Unknown This test statistic has a t distribution with n - 1 degrees of freedom. • Rejection Rule One-TailedTwo-Tailed H0: μ<μ0 Reject H0 if t > tα H0: μ>μ0 Reject H0 if t < -tα H0: μ=μ0 Reject H0 if |t| > t

  13. 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

  14. Hypothesis Tests About the Difference Between the Means of Two Populations: Independent Samples • Hypotheses H0: μ1 - μ2< 0 H0: μ1 - μ2> 0 H0: μ1 - μ2 = 0 Ha: μ1 - μ2 > 0 Ha: μ1 - μ2 < 0 Ha: μ1 - μ2≠ 0 • Test Statistic Large-Sample Small-Sample

  15. 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:

  16. Contoh Soal: Express Deliveries Delivery Time (Hours) District OfficeUPXINTEXDifference 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

  17. Contoh Soal: Express Deliveries • Inference About the Difference Between the Means of Two Populations: Matched Samples • ConclusionReject H0. There is a significant difference between the mean delivery times for the two services.

  18. Selamat Belajar Semoga Sukses

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