An article about using a diagnostic test (helical computed tomography) to screen adult smokers for lung cancer warned that a negative test may cause harm by providing smokers with false reassurance, and a false-positive test results in an unnecessary operation opening the smoker’s chest (Mahadevia et al., JAMA , vol. 289, pp. 313–322 , 2003). Explain what false negatives and false positives mean in the context of this diagnostic test.