To calculate the standard error (i.e. standard deviation of sampling distribution) of a normal Z distribution, we use the population standard deviation, σ, and the sample size, n (SE = σ/√n). When we do not know σ, we can use the sample standard deviation, s, to estimate σ. Replacing σ with s introduces extra error. To account for this extra error, we work with a t-distribution rather than a standard normal Z distribution (the t-distribution is shorter and flatter in the center and has heavier tails compared to the normal Z distribution). As a result, the formula for standard error becomes (s/√n) rather than (σ/√n). As your sample size increases, the shape of the t-distribution begins to resemble the standard normal distribution (looking at a t-table, you can see this happens when degrees of freedom (df) > 30).
