Hypothesis
Testing: TTest

The process of hypothesis testing
when we don't know the population standard deviation
is the same as the process when we do know it, except
for two changes:
 The standard error is calculated differently.
 (Classical Approach) The critical region is
different. We need to know the degrees of freedom.

We have the same four steps:
 State the Hypotheses:
This step is the same as with the ZStatistic. We state
null and alternative hypotheses.
 (Classical Approach)
Set the decision criteria:
 Specify alpha, the significance level.
This is the same as with the ZStatistic. For example:
 Determine the critical value of T.
Here there is a new complication in using T: There
isn't just one Tdistribution that we use to determine
the critical value of T. There is a whole family of
distributions. The distribution depends on the "degreesoffreedom",
which is simply equal to one less than the sample
size. That is:
We locate the critical T value by using the specified
alphalevel and df in the T distribution table in
the Appendix.
(Contemporary Approach)
The computer uses the Tdistribution and the degreesoffreedom
to calculate the exact probability of the result of the
experiment.
 Gather Data.
This step is the same as with the ZStatistic.
 Evaluate the Null Hypothesis.
We calculate the standard error of the mean using the
sample's standard deviation. Then we calculate T.
 Determine the standard error of the mean. The
standard error is calculated by the formula:
 Calculate the TestStatistic. The T formula
is:
 Make a decision:
 Classical Approach: We find the P value
for the obtained T and known df, comparing it to
the critical T value. If the obtained P is less
than alpha, we reject the null hypothesis.
 Contemporary Approach: The computer calculates
the P value. We report it and let the reader/listener
decide.
Next Topic: TTest Example
Outline of this Lecture
