8. Using the given information below, answer (a) to () Consider a random sample

Question

8. Using the given information below, answer (a) to () Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown. Condition Condition Present 110 20 130 Absent 20 Row Total 130 Test Result + Test Result- 70 200 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities: (a) P(+ I condition present); this is known as the sensitivity of a test. (b) P(- I condition present); this is known as the false-negative rate. (c) P(-I condition absent); this is known as the specificity of a test. (d) P(+ I condition absent); this is known as the false-positive rate (e) P(condition present and + ): this is the predictive value of the test. (t) P(condition present and ).

Explanation / Answer

(A)

Out of 130 patients with condition, 110 have positive test results so the required probability is

P(+ | condition present) = 110 /130 = 11 /13

(B)

Out of 130 patients with condition, 20 have negative test results so the required probability is

P(- | condition present) = 20 /130 = 2 /13

(C)

Out of 70 patients with condition absent, 50 have negative test results so the required probability is

P(- | condition absent) = 50 /70 = 5/7

(D)

Out of 70 patients with condition absent, 20 have positive test results so the required probability is

P(+ | condition absent) = 20 /70 = 2/ 7

(E)

Out of 200 patients, 110 have condition present and test positive so

P(condition presnet and +) = 110 /200 =0.55

(F)

Out of 200 patients, 20 have condition present and test negative so

P(condition presnet and -) = 20 /200 =0.10

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