Question

Provide one example each of both a Type I and Type II error that could occur
when running predictive engines relevant to sports betting. Which is likely to
be more costly and why?

Answer 1

A Type I error is the rejection of a true null hypothesis. So, in case of running a predictive engines relevant to sports betting, consider the null hypothesis, "Team A wins". The predictive engine predicts "Team A will NOT win", that is, it arejects the null hypothesis. But actually Team A wins. In this case our null hypothesis is true, but the predictive engine rejects it.

A Type II error is the non-rejection of a false null hypothesis. So, consider the same null hypothesis, "Team A wins". The predictive engine predicts "Team A will win", that is it failed to reject null hypothesis. But actually Team A lose. In this case our null hypothesis is NOT true, but the predictive engine failed to rejects it.

Consider the cases

(a) To judge whether someone is guilty

H0: A convict is innocent vs H1: He/She is guilty

Here Type I error is more critical (that is, rejecting he/she is innocent when he is actually innocent. From a courtroom point of view, it is not desirable to declare someone guilty when he/she is actually innocent).

(b) To trigger the fire alarm, we want to test if there is fire or no fire

H0: There is No fire vs H1: There is fire

Clearly Type II error is more critical (that is, accepting H0 when there is actually fire).

So, generally both errors can be costly based on the hypothesis. But in most of the cases Type I error is generally more serious.