4. Summary of Methods

How Do I Determine Whether the Student’s 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.