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MINI PROJECT 5 MEDICAL TESTING The incidence of a disease in a particular sample and the accuracy of current testing is described by the numbers in the 2-way table below. Does Not Has Disease Total Have Disease Test Positive 195 290 Test Negative in 150,000 150,005 Total 200 150,095 150,295 1. Use the data to estimate the following marginal probabilities; they are called marginal since they are calculated using the numbers in the margins of table (the row & column totals). a. P(a randomly selected person has the disease) = b. P(a randomly selected person tests positive) = c. Are these empirical or theoretical probabilities? Explain. d. Why are these probabilities "estimates"? 2. Use the disease data to estimate the following conditional probabilities; they are called con- ditional since the probabilities depend on which group an individual is in. a. P(a randomly selected person with the disease tests positive) number with disease who test positive number with the disease b. P(a randomly selected person without the disease tests negative) number without disease who test negative number without the disease Learning Through Practice: Statistical Reasoning 211Mini Project 5 c. P(a randomly selected person with the disease tests negative) = d. P(a randomly selected person without the disease tests positive) = e. Parts a and b give the accuracy of the test, so we could say that the test is at least 97.5% accurate. The calculation in Parts c and d represent errors. In particular, Part c is a false negative. Fill in the blanks: The probability this test results in a false negative is The probability this test results in a false positive is 3. After a medical test has been developed and its accuracy determined, the question of inter- est is the chance that someone actually has the disease if they test positive. Use the data to estimate the following a. P(someone has the disease given they tested positive) = Write a sentence to interpret this number in context. b. P(someone does not have the disease given they tested negative) = Write a sentence to interpret this number in context. c. Practically speaking, what should someone do if a test comes back positive? 212 Learning Through Practice: Statistical Reasoning