654 / 762
654
Chapter 14: Hypothesis Tests – Small Samples
For a specified significance level
, reject the null hypothesis if
the computed test statistic value
is greater than -
.
Conclusion
: ……….
Note:
This is a left-tailed test because the direction of the inequality sign in
the alternative hypothesis is to the left.
(c) Two –tailed Test
0
> 0
̅
√ ⁄
For a specified significance level
, reject the null hypothesis if
the computed test statistic value
is less than
or if it is greater
than
. This is equivalent to checking whether |
t
| >
.
Conclusion
: ……….
Note:
This is a two-tailed test because of the not-equal-to symbol in the
alternative hypothesis. Also, note that the level of significance is shared
equally when finding the critical
t
value (
).
Example 14-12
:
Adietitian wanted to measure the weight loss for nine
male patients who were undergoing a weight loss program. The patients
were weighed at the beginning of the program and the weights were
recorded. At the end of the weight loss program, the patients were again
weighed and weights were recorded.
Table 14-4
shows the before-and-after measured weights, in pounds, for the
nine patients. Test at the 5% level of significance for this set of dependent
data to determine whether the diet program was effective in reducing the
weights of the patients.