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Chapter 14: Hypothesis Tests – Small Samples
:
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
is greater than +
.
Conclusion
: ……….
Note
: This is a right-tailed test because the direction of the inequality sign
in the alternative hypothesis is to the right.
Example 14 -1
: A publication reported that the per capita consumption of
all alcoholic beverages in the state of Florida is 2.61 gallons per year,
ranking it in the bottom 30% nationally. A researcher selected a sample of
18 residents of Florida and found a mean consumption of 2.89 gallons per
year for the sample, and wonders whether the consumption is higher than
that reported. Test at the 5% level of significance. Assume that the standard
deviation of the consumption for the sample is 0.30 gallons.
Summary Information
:
=18,
= 0.30 gal,
= 0.05,
̅
(sample mean) =
2.89 gallons,
= 18 – 1 = 17,
=
= 1.7396, and
= 2.61 gal.
Also,
√ ⁄
= 0.0707.
Since the researcher would like to establish that the average consumption is
higher, the alternative hypothesis should reflect this belief.
Solution:
:
2.61 gallons
:
> 2.61 gallons
:
t
=
( ̅
) ( √ ⁄ )
⁄
= (2.89 – 2.61)/0.0707 = 3.9604.