Question

A new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcher selects a random sample of 2000 adults and finds (by other means) that 2% have this type of cancer. Each of the 2000 adults is given the test, and it is found that the test indicates cancer in 99% of those who have it and in 2% of those who do not. Based on these results, what is the probability of a randomly chosen person having cancer given that the test indicates cancer?

Answer #1

answer = 0.5025

A new, simple test has been developed to detect a particular
type of cancer. The test must be evaluated before it is put into
use. A medical researcher selects a random sample of 2,000 adults
and finds (by othermeans) that 3% have this type of cancer. Each
of the 2,000 adults is given the test, and it is found that the
test indicates cancer in 97% of those who have it and in 1% of
those who do not.
Based...

Suppose a test for cancer is given. If a person has cancer, the
test will detect it in 96% of the cases; if the person does not
have cancer, the test will show a positive result 1% of the time.
If we assume that 12% of the population taking the test actually
has cancer, what is the probability (rounded to the nearest
percent) that a person taking the test and obtaining a positive
actually has cancer?

"To diagnose colorectal cancer, the hemoccult test is
conducted to detect occult
blood in the stool. For symptom-free people over 50 years old who
participate in
screening using the hemoccult test, the following information is
available.
The probability that one of these people has colorectal cancer is
0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that he
will have a
positive hemoccult test. If a person does not have colorectal
cancer, the
probability is 3...

A new, non-invasive colon cancer screening method boasts a
sensitivity of 99%. That is, given that a patient has colon cancer,
the screening method has a 0.99 probability of yielding a
positive test. The test is also 90% specific, meaning that if a
person without colon cancer is screened, there is a 0.9 probability
of a negative test result. Among the population of adults
over 45 years of age, the proportion who have colon cancer is
0.0013 (thirteen out of...

"To diagnose colorectal cancer, the hemoccult test is
conducted to detect occult
blood in the stool. For symptom-free people over 50 years old who
participate in
screening using the hemoccult test, the following information is
available.
The probability that one of these people has colorectal cancer is
0.3 percent. If a
person has colorectal cancer, the probability is 50 percent that he
will have a
positive hemoccult test. If a person does not have colorectal
cancer, the
probability is 3...

A test for detecting cancer which appears to be promising has
been developed. It was found that 98% of cancer patients in a
hospital reacted positively to the test while 4% of those without
cancer reacted positively. 3% of the patients in the hospital have
cancer.
Let P(C) = Probability of a patient having cancer
Let P(NC) = Probability of a patient not having cancer
Let P(P+) = Probability of a patient getting a positive
result
Let P(P-) = Probability...

The sensitivity of a medical test refers to the test’s ability
to correctly detect ill patients who have the condition.
Mathematically, sensitivity is equivalent to the probability that
the test indicates a patient is ill given that the patient is ill.
The specificity of a medical test refers to the test’s ability to
correctly detect that a healthy patient does not have the
condition. Mathematically, specificity is equivalent to the
probability that the test indicates the patient is healthy given...

A new drug has been developed to treat a particular condition,
and it is alleged to be more effective than traditional treatment.
An experiment will be conducted to test whether the claim is true.
To perform the hypothesis test, a 99% confidence level is selected
for the hypothesis test. The new drug will be administered to a
sample of 200 individuals with the condition, selected at random.
Another 300 individuals are randomly selected to receive the
traditional treatment.
Of the...

A new drug has been developed to treat a particular condition,
and it is alleged to be more effective than traditional treatment.
An experiment will be conducted to test whether the claim is true.
To perform the hypothesis test, a 99% confidence level is selected
for the hypothesis test. The new drug will be administered to a
sample of 200 individuals with the condition, selected at random.
Another 300 individuals are randomly selected to receive the
traditional treatment.
Of the...

A new drug has been developed to treat a particular condition, and it is alleged to be more effective than traditional treatment. An experiment will be conducted to test whether the claim is true. To perform the hypothesis test, a 99% confidence level is selected for the hypothesis test. The new drug will be administered to a sample of 200 individuals with the condition, selected at random. Another 300 individuals are randomly selected to receive the traditional treatment.
Of the...

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