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Chapter 14: Hypothesis Tests – Small Samples
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Example 14 -7
: 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 equal variances.
Table 14-2
: Data for
Example14-7
Use the
P
-value approach to 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 both sample sizes are less than 30, then we can
apply the small sample
t
-test for the difference between two population
means.
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 14-15.