636 / 762
636
Chapter 14: Hypothesis Tests – Small Samples
:
(
)
P
-value = 0.0079 (from
Figure 14-12
)
For a significance level
= 0.01, reject the null hypothesis if the
computed
P
-value = 0.0079 <
= 0.01.
Conclusion
:
Since 0.0079 < 0.01, reject
. Thus, there is sufficient sample
evidence to conclude that that on average for this statistics course, the
female students spend more than male students on shopping at the beginning
of the semester, at the 1% level of significance.
Note:
Again, since the null hypothesis was rejected, there is a significant
differentiation for the difference between the sample means and the
postulated value of 0.
(b) Left –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 left-tailed test because the direction of the inequality sign in
the alternative hypothesis is to the left.
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.