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.

Null and alternative hypotheses

Two-tailed tests about a population mean involve the hypotheses

H0 :   μ  =  μ0
HA :   μ  ≠  μ0

where µ0 is the constant that we think may be the true mean.

In a one-tailed test, the alternative hypothesis involves only high (or low) values of µ, such as

H0 :   μ  =  μ0
HA :   μ  >  μ0