Econometric Theory/Statistical Inference/Hypothesis Testing

Basic Concepts
To conduct a successful hypothesis test, the following are required:

We need to have a null ($$H_0$$) and alternate ($$H_1$$) hypothesis.
 * Testable Hypothesis

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: A decision rule clearly delineates the:
 * Feasible test statistic
 * Its probability distribution is known when the null hypothesis ($$H_0$$) is true.
 * Its value can be calculated from the given sample data
 * Decision rule
 * Rejection region - the set of values of the test statistic for which $$H_0$$ is to be rejected.
 * Non-rejection region - the set of values of the test statistic for which the $$H_0$$ is to be retained.

Procedure for testing a hypothesis

 * 1) Formulate $$H_0$$ and $$H_1$$.
 * 2) Specify the test statistic and its distribution.
 * 3) Calculate the sample value of the test statistic under $$H_0$$ for the given sample data.
 * 4) Select a significance level (&alpha;) and determine the corresponding critical values (for the particular distribution).
 * 5) Apply the decision rule and state the conclusion (or inference) implied by the sample value of the test statistic.