1. To evaluate the performance of a new diagnostic test for disease X, the developer performed a trial on 100 people known to have disease X and 95 of them

have positive test results. The test is also performed on 200 control cases known to be free of disease X and 30 of them have positive test results. Based on these data, what is the sensitivity and specificity of the test? (10 marks) 2. Based on all the information currently available, you estimate that Mr. Chen has a 0.2 probability of having disease Y. You order a diagnostic test for disease Y which has a sensitivity of 95% and a specificity of 85%. (a) Suppose that the result comes back positive. Based on all the information now available, what is the probability that Mr. Chen has disease Y? Compute your answer to at least 4 decimal places. (5 marks) (b) On the other hand, suppose that the result comes back negative. Based on all the information now available, what is the probability that Mr. Chen has disease Y? Compute your answer to at least 4 decimal places. (5 marks) 3. A test with 95% sensitivity and 85% specificity is used to screen a population of 10,000 people for disease Z. Previous studies indicated that this population has a 10% prevalence rate for disease Z. What is the expected number of people in the population that will have test results that are correct? (5 marks)