A hypothesis test uses sample data to assess whether there is sufficient evidence against a statement about a population parameter. Null and alternative hypotheses **Alternative hypothesis** | **Test** | **Evidence sought** H_1:mu< _0 | Left-tailed | Unusually small sample means H_1:mu> _0 | Right-tailed | Unusually large sample means H_1:mu!= _0 | Two-tailed | Sample means far from _0 in either direction For a test of an unknown population mean, the point null is H_0:mu= _0. Tail direction is determined by H_1. Decision language - If the observation is sufficiently unlikely under H_0, reject H_0. - Otherwise, do not reject H_0. This is not proof that H_0 is true. - State the conclusion in the context of the population claim. The significance level alpha is the designed probability, or upper bound, of rejecting H_0 when H_0 is true. For a simple null with an exact continuous test, the rejection region is normally chosen to have probability alpha.

A hypothesis test uses sample data to assess whether there is sufficient evidence against a statement about a population parameter.

For a test of an unknown population mean, the point null is \(H_0:\mu=\mu_0\). Tail direction is determined by \(H_1\).

Null hypothesis

If the observation is sufficiently unlikely under \(H_0\), reject \(H_0\).

Otherwise, do not reject \(H_0\). This is not proof that \(H_0\) is true.

State the conclusion in the context of the population claim.

The significance level \(\alpha\) is the designed probability, or upper bound, of rejecting \(H_0\) when \(H_0\) is true. For a simple null with an exact continuous test, the rejection region is normally chosen to have probability \(\alpha\).

Alternative hypothesis	Test	Evidence sought
\(H_1:\mu<\mu_0\)	Left-tailed	Unusually small sample means
\(H_1:\mu>\mu_0\)	Right-tailed	Unusually large sample means
\(H_1:\mu\ne\mu_0\)	Two-tailed	Sample means far from \(\mu_0\) in either direction

Hypotheses, Tails and Significance

Hypotheses, Tails and Significance