2. Suppose that a certain test for lung cancer test has been found to have the f

Question

2. Suppose that a certain test for lung cancer test has been found to have the following reliability Among those who do have lung cancer, the test correctly detects 98% of the people who have lung cancer (a "true positive" result). Among those who do not have lung cancer the test correctly identifies 95% of the people as not having cancer (a "true negative" result). Statistics show that about 0.121% of the population has lung cancer a. Draw a tree diagram, labeling each edge with a probability Interpret the situation in terms of an ideal data set of 100 million people, and set up a two-way frequency table. b. tests positive tests negative total has lung cancer doesn't have lung cancer total 100,000,000 c. When an individual is given the test, what is the probability that the result is positive? d. Suppose that an individual is given the test for lung cancer and it claims to detect the disease, i.e. the test comes back "positive". What is the probability that the person actually has lung cancer? e. In light of part d, the advice to people who test positive might be"get tested again." If a person who doesn't have lung cancer is tested twice, what is the probability of testing positive (i.e. false positive) both times? Assume that the two tests are independent of one another f. Suppose that an individual is given the test for lung cancer and it comes back "negative". What is the probability that the person actually has lung cancer (i.e. it is a false negative result)?

Explanation / Answer

A - have lung cancer

B- test positive

a)

make yourself

b)

formula in excel

c)

probability the result is positive = 5112530/100 million = 0.0511253

d)

P(A|B) = P(A and B)/P(B) = 118580/5112530 = 0.023194

test +ve negative has lung cancer 118580 2420 121000 doesn't have lung cancer 4993950 94885050 99879000 5112530 94887470 100000000

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.