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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, H1 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.(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?

(e) John showed his report to Dr. Grey who tells him that since the probability of Type II error is only 0.2, it is therefore more likely than not that he carries gene X given the positive test report. Is this reasoning correct? Explain in no more than 3 sentences

Please answer only part d) and e) carefully

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