The Student’s-t distribution is most commonly used to represent the distribution of an uncertain population mean, given a sample mean and standard deviation. It is characterized by one parameter, the number of degrees of freedom, which equals the number of samples minus one. The t distribution is symmetric.
The t distribution is often used as follows:
where:
μ = the population mean;
X = the sample mean;
tc = the t-distribution for n-1 degrees of freedom, at a cumulative value of c;
sx = the sample standard deviation;
n = the number of samples; and
c = the desired confidence level.
