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Chapter 14: Hypothesis Tests – Small Samples
Example 14 -3
: A study was done on the media habits of American
children aged 8 to 18 and found that these children are engaged with media
on average at least 6 hours per day. After reviewing much literature on the
subject, a middle school teacher hypothesizes that children in her school
engage in far less media than the reported 6 hours per day because of the
amount of schoolactivities in which the students are involved. Data on 25
randomly selected students attending her schoolyielded a mean of 5.7
hours/day and a standard deviation of 1 hour/day. Test at the 1% level.
Summary Information
:
= 25,
= 1.00 hour,
= 0.01,
̅
(sample mean) =
5.7 hour,
=
– 1 = 25 – 1 = 24,
=
= 2.4922, and
= 6
hours. Also,
√ ⁄
= 0.2 hour.
Since the teacher would like to establish that the average engagement is less
than 6 hours, this should be reflected in the alternative hypothesis and thus,
this will be a left-tailed test.
Solution:
:
6 hours
:
< 6 hours
:
t
=
( ̅
) ( √ ⁄ )
⁄
= (5.7 – 6)/0.2 = -1.5.
: For a significance level of
= 0.01, reject the null hypothesis if the
computed test statistic value
= -1.5 < -
= -2.4922.
Conclusion
: Since –1.5 > -2.4922, do not reject
. That is, there is
insufficient sample evidence to support the claim that the average media
engagement for these children is less than 6 hours per day at the 1% level of
significance.
Note
: There is not a statistically significant difference between the sample
mean of 5.7 hours and the postulated value of the population mean of 6
hours. However, a practical difference indeed may not exist, because the
harmful/beneficial effects of 5.7 hours of media engagement versus 6 hours
are likely equivalent in a practical sense.