Student’s t Distribution

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 The square root of the variance of a distribution. The variance is the second moment of the distribution and reflects the amount of spread or dispersion in the distribution.. 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;

t_c = the t-distribution for n-1 degrees of freedom, at a cumulative value of c;

s_x = the sample standard deviation;

n = the number of samples; and

c = the desired confidence level.