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Chapter 14: Hypothesis Tests – Small Samples
655
Table 14-4
: Data for
Example14-12
Solution:
Since we would like to determine whether the program was effective in
reducing the weights of the patients, it would be convenient to use the
(after - before) weight differences.
We will use the differences (after - before) as the raw data in the test.
The (after – before) differences are given in
Table 14-5.
Table 14-5
: (After – Before) Differences for
Example14-12
For the differences we have,
̅
= - 98,
= 4.4441,
= 9. Also,
= 0.05,
= 9 – 1 = 8,
= 1.8596, and
√
= 1.4814.
Since we would like to establish whether the diet was effective, then we
should try to establish that
< 0 where
is the mean for the population
of the differences (after – before).
0
< 0
̅
√ ⁄
= (-98 – 0)/1.4814 =-66.1536
For a significance level
= 0.05, reject the null hypothesis if the
computed test statistic value
= - 66.1536 < -
= -1.8596.