631 / 762
Chapter 14: Hypothesis Tests – Small Samples
631
will follow a
-distribution with degrees of freedom
+
– 2.
These properties and conditions can aid us in performing hypothesis tests for
the difference between two independent population means for small
independent samples.
Next we will present the various tests for the difference between two
population means when the samples are small, the population variances are
unknown but equal, and the sampling populations are normally distributed.
Summary of Hypothesis Tests
(a) Right –tailed (one-tailed) Test
The subscripts 1 and 2 are used to represent population 1 and
population 2, respectively.
:
(
)
:
(
)
̅
̅
√
, where
is the pooled standard deviation.
D.R
: For a specified significance level
, reject the null hypothesis if
the computed test statistic value
where
–
2.
Conclusion
: ……….
Note:
This is a right-tailed test because the direction of the inequality sign
in the alternative hypothesis is to the right.
Note:
In the null hypothesis we have replaced the “=” sign with “
”. This
does not change the test procedure since during the process equality is
assumed.