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Chapter 14: Hypothesis Tests – Small Samples
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When we have independent samples, there is a procedure that we can use to
perform hypothesis tests for the difference between two population means
when the sample sizes are small and the population variances or standard
deviations are unknown.
The procedure assumes:
the samples are obtained from normal populations.
the populations have unknown but equal variances (standard
deviations).
the sample sizes are less than 30.
Assuming Equal Variance (Standard Deviation)
We will let
. Thus, assuming equal variances (standard
deviations), we have that the distribution of the differences of the sample
means will have a standard deviation which can be written as follows: