4 Understanding type I and type II errors is essential for a surgeon’s quality planning. Consider, for example, appendectomy operations. Following a diagnosis of appendicitis, removal of the appendix is necessary because of the risk of it bursting, causing potentially fatal poisoning of the blood. The surgical procedure is a relatively simple operation, but there is always a small risk with any invasive surgery. It is also an expensive procedure; in the USA around $4,500 per operation. Unfortunately, appendicitis is difficult to diagnose and the diagnosis is only 10 per cent accurate. However, a new technique claims to be able to identify 100 per cent of true appendicitis cases prior to surgery; this costs less than $250, which means that one single avoided surgery pays for around 20 tests.

(a) How does this new test change the likelihood of type I and type II errors?

(b) Why is this important?