Choosing Between z and t Distribution

The z and t distributions can estimate the mean of a population using a sample statistic. But how does one choose the appropriate distribution for a given dataset?

The z distribution is preferred for populations with a known standard deviation that is normally distributed or populations that have a sample size greater than 30.

However, the Student t distribution is preferred if the population standard deviation is unknown for a normally distributed population or if the population has a sample size greater than 30.

Symmetrically distributed datasets with very large sample sizes show less variability. For such datasets, the population mean estimated by both the z and t distributions are similar.

The z and t distributions are limited to random samples drawn from normally distributed populations. Thus, they cannot estimate the population mean for samples drawn from voluntary sample responses, convenience sampling, or skewed or unknown population distributions.

Therefore, nonparametric statistics or computer bootstrapping methods are used for populations that are not normally distributed and those populations that have a sample size less than or equal to 30.