Tests about numerical populations
The most important characteristic of a numerical population is usually its mean, µ. Hypothesis tests therefore usually question the value of this parameter.
A couple of examples are now shown in which the question of interest can be expressed in terms of hypotheses about a population mean, μ.
Null and alternative hypotheses
Both of the above examples involve tests of hypotheses
H0 : μ = μ0
HA : μ ≠ μ0
where µ0 is the constant that we think may be the true mean. These are called two-tailed tests. In other situations, the alternative hypothesis may involve only high (or low) values of µ (one-tailed tests), such as
H0 : μ = μ0
HA : μ > μ0