Question

Hi, I'm a finance major in a statistics class and I don't have a concrete understanding of some of the stuff we are doing in class. So for example, we normally calculate Z scores given an alpha level, but is it possible to do the opposite - calculate an alpha level given a Z score or a sample statistic critical value? Thanks!

Answer 1

Solution:

We can find the alpha level using the z-score or critical value. Let me explain it.

Suppose if we are given the z-score is 1.96, then the alpha can be found as:

Now if use the standard normal table, we will have:

This indicates the alpha level is 0.025, but please remember this is the area in the right tail.

Now, if we have two z-score values for the two-tailed test say -1.96 and 1.96. Then the alpha level is:

Therefore, here the significance level is 0.05

Hope this helps!