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 sM is the estimated standard error of the mean. If M = 15 and sM = 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.