625 / 762
Chapter 14: Hypothesis Tests – Small Samples
625
:
=
( ̅
) ( √ ⁄ )
⁄
= (35 – 32)/1.4 = 2.1429.
: For a significance level of
= 0.05, reject the null hypothesis if the
computed test statistic value
= 2.1429 < -
= -2.0639 or if
=
2.1429 >
= 2.0639. Alternatively, reject
if | 2.1429 | = 2.1429 >
2.0639.
Conclusion
: Since |2.1429| = 2.1429 > 2.0639 reject
. There is sufficient
sample evidence to refute the Dean’s claim. The sample evidence
does not support the Dean’s claim that the average distance commuting
students travel to the campus is 32 miles at the 5% level of significance.
Note
: There is a statistical significant difference between the sample mean
of 35 miles and the postulated value of the population mean of 32 miles.
Figure 14-9
displays the test statistic in relation to the rejection region.
Observe that the test statistic falls in the rejection region.