A jealous wife: The Choice of Significance Level

The most common choices of significance level are 0.01, 0.05, and sometimes 0.1. The significance level can be chosen based on the nature of the problem/area/… just like how we consider an event abnormal depending on the occasion.

For example, if I am to judge if a suspect is guilty of murder or not, then my is

which is the one that we want to reject if there is enough evidence against it. The alternative hypothesis is

I don’t want to convict a non-guilty person to death, so it is very hard to convince me that the suspect is guilty unless the evidence against him is clear. So I would use a very low significance level instead of a bigger value like or . This would create a smaller rejection region (the bigger , the bigger the area of the rejection region).

On the other hand, if a jealous wife is to judge whether her husband is cheating on her or not via hypothesis testing, then her is

which is the fact that she wants to reject. Her is

Since she is full of jealousy, it is likely that it is very easy to convince her that her husband is cheating on her. Hence, she would be more likely to use a bigger like which creates a bigger rejection region rather than using a lower significance level like or . Even though she uses , I think if a test can’t reject the null hypothesis, she will find another test after another test if all the tests before that fail anyway. And who knows, maybe she just concludes that he is cheating on her based on the evidence in her imagination without any statistical hypothesis testing?