Econometric Theory/Statistical Inference/Hypothesis Testing
< Econometric Theory  Statistical InferenceBasic ConceptsEdit
To conduct a successful hypothesis test, the following are required:
 Testable Hypothesis
We need to have a null ( ) and alternate ( ) hypothesis.
 Feasible test statistic
A test statistic is a random variable whose value for given sample data determines whether the null is rejected or retained. It is feasible when:

 Its probability distribution is known when the null hypothesis ( ) is true.
 Its value can be calculated from the given sample data
 Decision rule
A decision rule clearly delineates the:

 Rejection region  the set of values of the test statistic for which is to be rejected.
 Nonrejection region  the set of values of the test statistic for which the is to be retained.
Procedure for testing a hypothesisEdit
 Formulate and .
 Specify the test statistic and its distribution.
 Calculate the sample value of the test statistic under for the given sample data.
 Select a significance level (α) and determine the corresponding critical values (for the particular distribution).
 Apply the decision rule and state the conclusion (or inference) implied by the sample value of the test statistic.
NotesEdit
 The null hypothesis will always be the position where there is an equality (either strong or weak), and the alternate hypothesis will have the inequality.