Hypothesis Test

statistics

Definition

Hypothesis Test

A hypothesis testing procedure or hypothesis test is a rule that specifies:

1. For which sample values the decision is made to accept $H_0$ as true.
2. For which sample values $H_0$ is rejected and $H_1$ is rejected.

The goal of a hypothesis test is to decide, based on a sample from the population, which of two complementary hypothesis is true.

Sided Tests

During hypothesis testing for the population mean $\mu$, we distinguish between the following cases:

Left-sided Test

$$\text{under }{H}_0:\mu \ge {\mu }_0\text{ against the alternative }{H}_1:\mu <{\mu }_0$$

Right-sided Test

$$\text{under }{H}_0:\mu \le {\mu }_0\text{ against the alternative }{H}_1:\mu >{\mu }_0$$

Two-sided Test

$$\text{under }{H}_0:\mu ={\mu }_0\text{ against the alternative }{H}_1:\mu \ne {\mu }_0$$