**How Do I Determine Whether the Student’s ***t-*Distribution Is Appropriate?

*t-*Distribution Is Appropriate?

Usually this is determined by knowing if the population is *approximately* normal. In many cases the determination is based on the sample data alone. Consider looking at a boxplot or a dotplot of the sample data, but this will only really show if the data is clearly *not* normal, for instance if the plot shows strong asymmetry or outliers. You could construct a probability plot, but with a small sample size, the boxplot or dotplot is easier to construct.

### Use *z*, Not *t*; if σ Is Known

Recall, the Student’s *t*-distribution was created in order to handle the problem in estimating the population standard deviation, from a normal population. So if the population standard deviation σ is known, then use the normal distribution from which the data comes, rather than the approximation distribution of the Student’s *t*-distribution.