ABSTRACT
The t distribution is mainly used for testing hypotheses and finding confidence intervals for means, given small samples from normal distributions. For a single sample, has the t distribution with v=n−1 degrees of freedom (see notation above). So, e.g. if n=10, giving v=9, the γ=95% confidence interval for µ is . Given two samples of sizes n1 and n2, sample means and , and adjusted sample standard deviations s1 and s2, has the t distribution with v=n1+n2−2 degrees of freedom, where . So if the population means are denoted µ1 and µ2, then to test H0:µ1=µ2 against H1:µ1>µ2 at the 5% level, given samples of sizes 6 and 10, the critical region is , using v=6+10−2=14 and
. As with the normal distribution, symmetry shows that values are just the values prefixed with a minus sign.
