Of the two methods for making a statistical decision, the p-value approach is more commonly used and provided in published literature. However, understanding the rejection region approach can go a long way in one's understanding of the p-value method. In the video, we show how the two methods are related. Regardless of the method applied, the conclusions from the two approaches are exactly the same.

Video: The Rejection Region vs the P-Value Approach

Both approaches will ensure the same conclusion and either one will work. However, using the p-value approach has the following advantages:

• Using the rejection region approach, you need to check the table or software for the critical value every time you use a different \(\alpha \) value.
• In addition to just using it to reject or not reject \(H_0 \) by comparing p-value to \(\alpha \) value, the p-value also gives us some idea of the strength of the evidence against \(H_0 \).