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For small sample sizes, the mean shows a t-distribution (compare the
for large samples: in this case the means are distributed according
to a normal distribution). The reason for this is that the estimate s of
the standard deviation is not accurate enough. But again the assumption
is that the distribution of the data is approximately normal. The only
difference from the derivation for the large sample case is that, instead
of the z-scores, we will use the t-scores, which we can obtain from statistical
tables, or by using the Teach/Me distribution
calculator. The t-distribution
depends on the number of samples. Its parameter is called degree
of freedom, and it is equal to the number of samples minus 1: df =
n - 1.
For a detailed description of how to perform a t-test, please have a
look at the z-test section.
Last Update: 2005-Jul-16