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Chapter 14: Hypothesis Tests – Small Samples
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It will be assumed that the sampling distribution for the sample means is
approximately normally distributed. The tests require that the population
standard deviation
be unknown and the sample size be small (i.e.
n
< 30).
We refer to tests based on the statistic
̅
√ ⁄
as small-sample tests
because we are assuming that the sampling distribution for the sample means
has a
t
distribution. The test requires that the sample size
< 30 and
requires that the population standard deviation be unknown. We also
assume that the sampling distribution is normal.
Figure 14- 1
shows the experimental display of the sampling population
with its mean
and standard deviation
. Recall, for this case the sampling
population is assumed to be normally distributed.
Figure 14- 1:
Experimental Display for Sampling from
a population with mean
and standard
deviation
Following is a summary of the tests for a population mean under these
conditions.
Summary of Hypothesis Tests
(a) Right –tailed (one-tailed) Test