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Chapter 14: Hypothesis Tests – Small Samples
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Example 14-11
:
Recall from
Example 14 -7
that two methods were used
to teach an elementary statistics course. A sample of 17 scores was selected
for method A, and a sample of 16 scores was selected for method B.
Table
14-2
shows the summary results of the study done by the researcher for the
samples.
Assume that the distributions of the scores for bothmethods are normally
distributed with unequal variances. Test at the 1% significance level to
determine whether Method A was less effective than Method B.
Solution:
Let
be equal to the population average of the test scores using Method A.
Let
be equal to the population average of the test scores using Method B.
Since the distributions for both groups of test scores are assumed to be
normally distributed and the sample sizes are less than 30, then we can apply
the small sample
-test for the difference between two population means
with unequal variances.
To minimize the computations in the problem, we will use the
Small
Sample Test for the Difference betweenTwo Independent Means
workbook to help with the computations. The appropriate portion of the
workbook is shown in
Figure 14-23
.