2. Assume that 1% of the one million people living in a city are currently infected with COVID 19, Further 1. Suppose the test for a disease has a sensitivity of Boss, meaning that if that person has the disease, the result is assume that we test them with a test that is 99.9" accurate (99.9% sensitivity, 99.9% specificity). The positive 20%% of the time. The test has a specificity of 90%, so if the person doesn't have the disease, the test is contingency table below reflects the results. Respond to the questions below. Show your work. negative 905% of the time. Assume 10% of all people in this population have this disease. Infected Healthy |8401 Fill in the missing numbers in the breakdown below. Show your calculations. (6 x 0.5 = 3 pts) Positive COVID 19 Test True Positive False Positive Population 9.990 390 10,980 20,000 Negative COVID 19 Test False Negative True Negative 989,020 10 289 010 Total 10,000 990,000 1,000,000 3. Number of Infected People b. Number of Healthy People (1016 of Population) (90*6 of population) 3. If someone tests positive, what is the probability they are infected? This is the positive predictive value (PPV) [1 pt) (10/100) x 20 000 = 2 000 of the test. This may also be written as Plinfected | positive test). Round to 2 decimal places. (90/100) x 20 000 = 18 000 90 9816 b. If someone tests positive, what is the probability they are healthy? This is the folse discovery rate. This may c. Number of d. Number of e. Number of f. Number of also be written as Pihealthy | positive test). Round to 2 decimal places. (1 p) Positive Test Results Negative Test Results Positive Test Results Negative Test Results (80% of Infected Get (20% of Infected Get (10%% of Healthy Get a (90% of Healthy Get a a Positive Result) a Negative Result] Positive Result) Negative Result (80/100) x 2000= 1600 (20/100) x 2000 = 400 (10/100) x 1800 = 180 (90/100) x 18000= 1620 C. When we add together the PPV and the false discovery rate for any test, why is the sum always 1009%? 1 pt) d. What is the probability someone is healthy given that they test negative? This is the negative predictive value (NPV) of the test. This may be written as Pihealthy pegative test). Round to 3 decimal places. (1 px] True Positives (TP) False Negatives (FN) False Positives (FP) True Negatives (TN) 2. What is the probability that someone is infected given that they test negative? This is the folse omission rate. This may also be written as Plinfected | negative test). Round to 3 decimal places. (1 pt) g. Fill in the table based on the results above. (1 0 Has Disease (Infected) | Does Not Have Disease (Healthy) | Totals Test Positive 1600 180 f. When we add together the NPV and the false omission rate for any test, why is the sum always 1009%? Test Negative 400 (1 pt) Totals 20,000