1 Pertemuan 08 Pengujian Hipotesis 1 Matakuliah: I0272 – Statistik Probabilitas Tahun: 2005 Versi: Revisi

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa akan dapat memilih statistik uji hipotesis untuk suatu dan dua rataan.

3 Outline Materi Uji hipotesis nilai tengah Uji hipotesis beda nilai tengah

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 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). H 0 :  >  0 H 0 :  <  0 H 0 :  =  0 H a :   0 H a :   0

7 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 H 0 when it is true. A Type II error is accepting H 0 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 H 0 ” and not “accept H 0 ”.

8 Type I and Type II Errors Population Condition H 0 True H a True Conclusion (  ) (  ) Accept H 0 Correct Type II (Conclude  Conclusion Error Reject H 0 Type I Correct (Conclude  rror Conclusion Example: Metro EMS

9 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)

10 Hypotheses H 0 :   H a :   Test Statistic  Known  Unknown Rejection Rule Reject H 0 if |z| > z  Two-Tailed Tests about a Population Mean: Large-Sample Case (n > 30)

11 Test Statistic  Known  Unknown This test statistic has a t distribution with n - 1 degrees of freedom. Rejection Rule One-Tailed Two-Tailed H 0 :   Reject H 0 if t > t  H 0 :   Reject H 0 if t < -t  H 0 :   Reject H 0 if |t| > t  Tests about a Population Mean: Small-Sample Case (n < 30)

12 p -Values and the t Distribution The format of the t distribution table provided in most statistics textbooks does not have sufficient detail to determine the exact p-value for a hypothesis test. However, we can still use the t distribution table to identify a range for the p-value. An advantage of computer software packages is that the computer output will provide the p-value for the t distribution.

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

14 Selamat Belajar Semoga Sukses.