Hypothesis
Testing


Hypothesis
testing is an inferential procedure that uses sample data
to evaluate the credibility of a hypothesis about a population.

Put
simply, the logic underlying the statistical hypothesis
testing procedure is:
 State
the Hypothesis: We state a hypothesis (guess) about
a population. Usually the hypothesis concerns the value
of a population parameter.
 Define
the Decision Method: We define a method to make
a decision about the hypothesis. The method involves
sample data.
 Gather
Data: We obtain a random sample from the population.
 Make
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 foolproof method for doing
this: Errors can be made. Specifically, two kinds of errors
can be made:
 Type
I Error: We decide to reject the null hypothesis
when it is true.
 Type
II Error: We decide not to reject the null hypothesis
when it is false.

