Diagnostic tests of medical conditions can have several types of results. The te

Question

Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or mot a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (-) indicates that the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 200 patients, some of whome have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown Test Result 16 54 0 Assume the sample is representative of the entire population. Far a person selected st random, compute the tilowing probuabilies. Enter your answers fractions.) is representative of the entire population. For a person selected at a)P+I condition present); this is known as the senseivity of a test (b) R- I condition present); this is known gs the falise-negaive rate. (c) P-I condition absent); this is known as the specifloty of a test )P+I condsition absent); this is known as the false-postive rate e) Pcondition present and +) this is the predictive value of the test. 054 ) condition present and-). Noed Help? HANNSpree

Explanation / Answer

Note that we have to enter the answers in form of fractions here as given in the problem

a) Using bayes theorem the probability here is computed as:

P( + | condition present ) = n( + , condition present ) / n( present ) = 107 / 123

b) Using bayes theorem the probability here is computed as:

P( - | condition present ) = n( - , condition present ) / n( present ) = 16 / 123

c) Using bayes theorem the probability here is computed as:

P( - | condition absent ) = n( - , condition absent ) / n( absent ) = 54 / 77

d) Using bayes theorem the probability here is computed as:
P( + | condition absent ) = n( + , condition absent ) / n( absent ) = 23 / 77

e) P ( condition present and + )

= n ( condition present , + ) / Total frequency

= 107 / 200

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