1. The results of a trial used to determine the capabilities of a new diagnostic test are shown in Table 1. Use the empirical probabilities obtained from the table to calculate the positive predictive value for the diagnostic test.
Table 1

2. The results of a trial used to determine the capabilities of a new diagnostic test are shown in Table 2. Use the empirical probabilities obtained from the table to calculate the positive predictive value for the diagnostic test.
Table 2

3. Suppose that 500 athletes are tested for a drug, 1 in 20 has used the drug, and the test has a 99% specificity and a 100% sensitivity. If an athlete in the group tests positive, what is the probability that they have used the drug?
4. Recent studies have indicated that polygraph tests have a sensitivity of .88 and a specificity of .86. (Currently, polygraph tests are admissible as evidence in court in 19 U.S. states.) Suppose that a robbery is committed and polygraph tests are given to 10 suspects, 1 of whom committed the crime. If the polygraph test for a person indicates that they are guilty, what is the probability they are actually guilty?

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Does Not Have Condition Has Condition Total Test positive Test negative 19 19 10 981 980 Total 990 10 1000 Has Condition Does Not Have Condition Total Test positive Test negative 20 13 77 80 84 Total 16 100