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.
