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Chapter 14: Hypothesis Tests – Small Samples
(c) Two –tailed Test
:
=
0
(where
0
is a specified mean value)
:
0
:
t
=
( ̅
) ( √ ⁄ )
⁄
for
unknown and
< 30
: For a specified significance level
, reject the null hypothesis if
the computed test statistic value
< -
⁄
or if
>
⁄
(this is
equivalent to
>
⁄
).
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
value (
⁄
).
Example 14 -5
: The dean of students of a four-year college claims that the
average distance commuting students travel to the campus is 32 miles. The
commuting students feel otherwise. A sample of 25 commuting students
was randomly selected and yielded a mean of 35 miles and a standard
deviation of 7 miles. Test the dean’s claim at the 5% level of significance.
Summary Information
:
= 25,
s
= 7,
= 0.05,
̅
(sample mean) = 35,
⁄
=
= 2.0639, and
= 32. Also,
√ ⁄
= 1.4.
This will be a two-tailed test, since the students feel that the dean’s claim is
not correct.
Observe that whether the students feel that the average distance is less than
32 miles or more than 32 miles is not specified.
Solution:
:
= 32 miles
:
32 miles