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 negative rate, p(- | i) to be less than 0.03. if the false positive rate is greater than 0.03, they will create a new test.

the manufacturer will need to ▼ create a new test, because the false negative rate is ▼ options: 0.02, which is less than 0.03; 0.07, which is greater than 0.03; 0.23, which is greater than 0.03

Explanation:

Step1: Calculate the false - negative rate

The false - negative rate \(P(-|I)\) is calculated by the formula \(P(-|I)=\frac{\text{Number of False Negatives}}{\text{Total Number of Infected}}\).
The number of false negatives is \(5400\), and the total number of infected is \(17600 + 5400=23000\).
So \(P(-|I)=\frac{5400}{23000}\approx0.23\).

Step2: Analyze the result

Since the manufacturer wants \(P(-|I)<0.03\), and \(0.23>0.03\), they will need to create a new test.

Answer:

The manufacturer will need to create a new test, because the false negative rate is \(0.23\), which is greater than \(0.03\).