Does this mean that we have to make a sampling distribution every time that we want to test an hypothesis? That would be a lot of work!

Fortunately, sampling distributions for different statistics have known shapes. Mathematicians, using calculus, derived the mathematical functions of these known shapes and used them to calculate the area under the curve (probability) at specific intervals. This is how the tables of critical values for each statistic were derived. We use the tables for our hypothesis tests, rather than making our own sampling distributions.

We have different tables for different statistics. That is because the shape of the sampling distribution varies for different statistics. Let's look at the sampling distributions for some commonly used descriptive and inferential statistics.