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