# Econometric Theory/Statistical Inference/Hypothesis Testing

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## Basic Concepts[edit]

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.
- Non-rejection region - the set of values of the test statistic for which the is to be retained.

## Procedure for testing a hypothesis[edit]

- 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.

## Notes[edit]

- 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.