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