Question

3. TestX has created a screening tool, 'iTest', to test for the presence of a gene, Gene X, in men. After screening, the patient receives a test report, which could be one of two kinds: a positive one or a negative one. One can interpret the screening tool iTest as a hypothesis testing procedure for testing the null 'Ho: The patient does not carry the gene X', against the alternative, 'Hi The patient carries the gene X'. A positive test report is then equivalent to rejecting the null, while a negative test report is equivalent to failing to reject the null. Seen this way, it is known that the probability of Type I error when using iTest is 0.05, while the probability of Type II error is 0.2. It is also known that exactly 1% of men at the age of 20 who participate in iTest screening carry the gene X. John Doe is a 20 year old man who has just finished an iTest screening 2(a) Before John receives the tstwhat is the probability that he does indeed carry gene X? 3(b) What is the probability of the test report being positive given that John does not in fact carry gene Xi? 3(c) What is the probability of the test report being positive given that John does in fact carry gene X? 9 (d) John has received his test report and it is positive. What is the probability that John does indeed carry gene X given that he received a positive test report?

Answer 1

) BePote John éeceives -the. test tepatt these is exactly i% (that is iïnlooj Man at %ge op 20 who participate in 1 Tes+ SCTeening cat-ty the gene x Let D is the even Sanaomly 6elicted ndiuidual has Patticipade in ỉTest t that q Test«epat being Positive given thet John P Ceejecting Ho lHo is true does not in Pact coatty gene x1 c) PLtest tepatt being Positive given that John does infact Cene x ] P Laccepting Ho/H, is true] 0-38