Answer to Question #166476 in Statistics and Probability for phemelo mongae

Question

. An X-ray test is used to detect a disease that occurs, initially without any symptoms, in 3% of the population. The test has the following error rates: • 7% of people who are disease free have a positive reaction; • 2% of the people who have the disease have a negative reaction. A large number of people are screened at random using the test, and those with positive reaction are taken for further examination. (a) What proportion of people who have disease are correctly diagnosed? (b) What proportion of people with a positive reaction actually have the disease? (c) What proportion of people with negative reaction actually have the disease? (d) What proportion of the test conducted give incorrect diagnosis?

Answer 1

1. 98%, because from the condition 2% of the people who have the disease have a negative reaction
2. 93%, because from the condition 7% of people who are disease free have a positive reaction
3. 2%, because from the condition 2% of the people who have the disease have a negative reaction
4. 7 + 2 = 9%