Statistical hypothesis testing arises in the context in which we observe
a random sample of the values of a random variable and from the observations
we wish to decide, in a reasoned manner,
whether to accept (non-reject) a given hypothesis, called the Null hypothesis,
concerning the distribution of
the random variable or whether to reject that hypothesis in favor of an Alternative
hypothesis also concerning the distribution of the random variable.

To accomplish an hypothesis test, we formulate a test statistic which is a function
of the observed values. We partition the possible values the test statistic can take
into two sets. If the value of the test statistic falls in the first set, called the critical
region, we will
reject the Null hypothesis in favor of the Alternative hypothesis. If the value of the
test statistic falls in the second set, called the acceptance region,
we will reject the Alternative hypothesis in
favor of the Null hypothesis.

The discipline of statistics gives us guidelines for how to design a test statistic and
how to define the critical region and acceptance region.