Alternative Hypothesis/Examples/Arbitrary Example 1

Examples of Alternative Hypothesis

Let $\delta$ be a hypothesis test.

Let $H_0$ and $H_1$ be the null hypothesis and alternative hypothesis of $\delta$ respectively.

Let $\theta$ be the test statistic which is being used to determine whether $H_0$ or $H_1$ holds.

Let the null hypothesis state that $T = 2$:

$H_0: \theta = 2$

The alternative hypothesis may be, for example:

$H_1: \theta \ne 2$

or that:

$H_1: \theta > 2$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hypothesis testing
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hypothesis testing