Question

a medical test manufacturer did a trial of a new virus screening test. 100,000 people took the test, and they already knew from other testing whether or not each person was infected with the virus.

	test positive (+)	test negative (-)
not infected (ni)	1,800	75,200

the manufacturer wants the false positive rate, ( p(+ | ni) ) to be less than 0.04. if the false positive rate is greater than 0.04, they will create a new test. will they need to create a new test?

this manufacturer

• will need to
• x will not need to

create a new test, because the false positive rate is ( \boxed{0.02} ), which is less than 0.04

Explanation:

Step1: Calculate the number of not - infected people

The total number of people is \(N = 100000\). The number of infected people is \(17600+5400=23000\). So the number of not - infected people is \(NI=100000 - 23000=77000\).

Step2: Calculate the false - positive rate

The false - positive rate \(P(+|NI)\) is the number of false - positives (people who are not infected but test positive) divided by the number of not - infected people. The number of false - positives is \(1800\). So \(P(+|NI)=\frac{1800}{77000}\approx0.0234\)

Answer:

Since \(P(+|NI)\approx0.0234<0.04\), they will not need to create a new test.