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Chapter 14: Hypothesis Tests – Small Samples
617
Since we would like to establish that the mean SCE for the veterans is
greater than that produced by the control group, the alternative hypothesis
should reflect this belief.
Solution:
(a) Right –tailed (one-tailed) Test
:
8.24
:
> 8.24
:
t
=
( ̅
) ( √ ⁄ )
⁄
= (10.99 – 8.24)/0.6226 = 4.4170.
: For a significance level of
= 0.05, reject the null hypothesis if the
computed test statistic value
= 4.4170 > +
= 1.7139.
Conclusion
: Since 4.4170 > 1.7139, reject
. There is sufficient sample
evidence to confirm the claim. That is, there is sufficient sample evidence to
claim that the average SCE is greater than 8.24 at the 5% level of
significance.
Note
: There is a statistical significant difference between the sample mean
of 10.99 and the postulated mean of 8.24.
Figure 14-4
displays the test statistic in relation to the rejection region.
Observe that the test statistic falls to the far right in the rejection region.