Final answer:
The important test for all family members to have in order to confirm the presence or absence of a Mycobacterium tuberculosis infection is the Purified protein derivative (PPD) test.
Step-by-step explanation:
The test that is important for all family members to have in order to confirm the presence or absence of a Mycobacterium tuberculosis infection is the Purified protein derivative (PPD) test. This test is a type of tuberculin skin test where bacterial proteins from M. tuberculosis are injected into the skin. A positive result indicates that the patient has been exposed to the bacteria and exhibits a cellular immune response to it. It is important to note that a positive PPD test does not necessarily mean that the patient is currently infected with active TB.