b) If a person tests negative for the virus, what is the probability that the person really is not infected.(This is called the "negative predictive value")c) Examine the "Infected" column of the table. If a person is actually infected, what is the probability thattheir test will be positive?(This is called test's "sensitivity")d) If a person is actually not infected, what is the probability that their test will be negative?%(This is called the test's "specificity") A certain affects virus 0.4% of the population (in a population of 100,000 people, 400 will be infected withthe virus). A test used to detect the virus in a person is positive 87% of the time if the person has the virus(true positive) and it is positive 14% of the time if the person does not have the virus (false positive). Fill inthe remainder of the following table and use it to answer the questions below.InfectedNot InfectedTotalPositive TestNegative TestTotal40099,600100,000

Solution: It is given that, the test is positive 87% of the time if the person has the virus. It is given that (the total of infected column) 400 people are infected. That is, 87% of these 400 people will test positive. 0.87*400 = 348 infected people will test positive. Out of 400 people, remaining (400-348 =) 52 people will test negative even though they are infected. Total Not infected people are given to be 99600 and it is given that the test is positive for 14% of the time if the person does not have the virus. 0.14*99600 = 13944 non infected people will test positive. Out of 99600 people, remaining (99600 - 13944=) 85656 people will test negative who are not infected. Part a) The table will be as follows: Infected Not infected Total Positive Test 348 13944 14292 Negative test 52 85656 85708 Total 400 99600 100000 Part b) If a person tests negative for a virus, the probability that the person is really not infected, is required. It can be written in terms of conditional probability as P(Not infected | Negative Test) and it can be calculated as follows: To convert this probability into percentage, we multiply it by 100. 0.999393*100 = 99.9393 Thus, the negative predictive value is 99.9393%. Part c) If a person is actually infected, the probability that their test will be positive, is required. It can be written in terms of conditional probability as P(Positive Test | Infected) and it can be calculated as follows: Multiplying it by 100, it becomes, 0.87*100 = 87 Thus, the sensitivity of this test is 87%. Part d) If a person is actually not infected, the probability that their test will ne negative, is required. To convert it into percentage, multiply it by 100. (0.86*100 = 86) Thus, the specificity of this test is 86%.

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Statistics

A certain affects virus 0.4% of the population (in a population of 100,000 people, 400 will be infected with the virus). A test used to detect the virus in a person is positive 87% of the time if the person has the virus (true positive) and it is positive 14% of the time if the person does not have the virus (false positive). Fill in the remainder of the following table and use it to answer the questions below. Infected Not Infected Total Positive Test Negative Test Total 400 99,600 100,000

A certain affects virus 0.4% of the population (in a population of 100,000 people, 400 will be infected with the virus). A test used to detect the virus in a person is positive 87% of the time if the person has the virus (true positive) and it is positive 14% of the time if the person does not have the virus (false positive). Fill in the remainder of the following table and use it to answer the questions below. Infected Not Infected Total Positive Test Negative Test Total 400 99,600 100,000

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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