The One Sample
tTest is a hypothesis
test used to test the mean
of a small sample taken from a population
with a normal distribution against a specified
value. The hypothesis is:
H_{0} the population mean equals
a specified value
H_{1} the popular mean is [equal
to/less than/greater than] a specified
value
The test is:
where:

sample mean 
μ _{0} 
specified value 
s 
sample standard deviation 
n 
sample size 
The critical value of the t statistic t_{0}
can be found in t
distribution tables, or the
pvalue
can be found using the Excel function:
=TDIST(t_{0},
ν
,
Tails)
The number of
degrees of freedom 'ν
' is n  1, the number of tails is 1 for
a one
sided test and 2 for a two
sided test.
The ttest requires that the population
conforms to a normal
distribution.
