# General Formula for Testing Hypotheses (2 of 3)

The

t rather than the

z (normal) distribution is used if the
standard error has to be estimated from the data. The formula then
becomes:

(The one exception to this rule you will encounter is that in
tests of

differences between proportions,
z is used even when the standard error is estimated.) For this
example, the formula is:

where s

_{M} is the estimated standard error of the mean.
If M = 15 and s

_{M} = 2, then t = 2.5. If N were 12 then the

degrees of freedom would be 11. A

t table can be used to calculate that the
two-tailed probability value for a t of 2.5 with 11 df is 0.0295. The
one-tailed probability is 0.0148.