Question

MATH 227 - Introduction to Probability and Statistics Module 5 Homework Name: Activity 2: Coronavirus Testing Assume there is a test for the SARS-CoV-2 virus (the virus that causes COVID-19) that is 98% accu- rate; i.e. if someone has the SARS-CoV-2 virus the test will be positive 98% of the time, and if one does not have it, the test will be negative 98% of the time. Assume further that 0.5% of the population actually has the SARS-CoV-2 virus. Imagine that you have taken this test and your doctor somberly informs you that you've tested positive. How concerned should you be? To answer this, let's make a table for a hypothetical town. Suppose the population of the town is 10,000 Calculate how many have the virus (0.5% of the population) and how many do not (99.5% of the population). Write your figures in the table below. Determine how many will test positive and how may will test negative (98% accurate). Do this separately for the "Has HIV" group and the "No HIV" group. Write your figures in the table below. Has Virus No Virus (0.5%) (99.5%) Totals Positive Negative Totals 10,000 a. Based on the figures from your table, calculate the probability that the test is positive given that the person has the virus, P(Posn). Does your calculation agree with the 98% accuracy rate? If not, go back and check your calculations b. Now calculate the probability that a person has the virus given that the test was positive, PCV Por), c. How does the result from part (b) compare with what you expected? Would this increase or decrease your worry if you got a positive test? d. Can you explain why the result was different than what you expected?

Answer 1

low d) But this case, ie the probability is low because the number of posinue cases are very compared to the no nous cases. Here the type I essor is high among cases 199 were total people who has nous is only 50, So the result is different from expected- total 248 tve as an high as wrongly classified to ave whereas