Understanding type I and type II errors is essential for surgeons’ quality planning. In appendectomy operations, for example, removal of the appendix is necessary because of the risk of it bursting and 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 expensive; in the US around $4,500 per operation. Unfortunately, appendicitis is difficult to diagnose; 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. The new technique 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?