testing is an inferential procedure that uses sample data
to evaluate the credibility of a hypothesis about a population.
simply, the logic underlying the statistical hypothesis
testing procedure is:
the Hypothesis: We state a hypothesis (guess) about
a population. Usually the hypothesis concerns the value
of a population parameter.
the Decision Method: We define a method to make
a decision about the hypothesis. The method involves
Data: We obtain a random sample from the population.
a Decision: We compare the sample data with the
hypothesis about the population. Usually we compare
the value of a statistic computed from the sample data
with the hypothesized value of the population parameter.
- If the
data are consistent with the hypothesis we conclude
that the hypothesis is reasonable.
- If there
is a big discrepency between the data and the hypothesis
we conclude that the hypothesis was wrong
- The purpose
of hypothesis testing is to make a decision in the face
of uncertainty. We do not have a fool-proof method for doing
this: Errors can be made. Specifically, two kinds of errors
can be made:
I Error: We decide to reject the null hypothesis
when it is true.
II Error: We decide not to reject the null hypothesis
when it is false.