t-procedures

t distributions are similar to normal distributions, however they have a greater spread, with more area in the tails and less in the centre. This difference in shape is due to the fact that substituting s for σ in the formula for the standard deviation of x introduces more variability into the possible values for x.
A t(k) distribution becomes more and more similar to a normal distribution as k increases. For this reason, z can be used for very large samples even when σ is unknown.

Robustness of t-procedures
t-procedures are more robust for samples with more observations.
They are not robust against outliers, as outliers have the potential to greatly influence x.
They are somewhat robust against skewedness.

The general guidelines for one-sample t-procedure robustness are:
if n < 15 use the t-procedures only if the sample's distribution is very close to normal.
if n > 15 use the t-procedures if there are no outliers and the sample's distribution is not strongly skewed
if n > 40 the t-procedures can be used even for clearly skewed data as long as there are no extremely influential outliers.