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