College false positive problems, solved and explained

Recent questions in False Positive

Brooklynn Hubbard 2022-05-10 Answered

in order to remember stuff i need to understand their reason. Right now i cannot remember what is type 1 error and what is type 2 error why is the reason type 1 is false positive?

Karissa Sosa 2022-05-10 Answered

"A certain disease has an incidence rate of 2%. If the false negative rate is 10% and the false positive rate is 1%, compute the probability that a person who tests positive actually has the disease."
Why do we need to use Bayes' Theorem for this question?

Adelyn Rodriguez 2022-05-09 Answered

Descartes rule of sign can be used to isolate the intervals containing the real roots of a real polynomial. The rule bounds the number of roots from above, that is, it is exact only for intervals having zero or one root. In methods like VCA, VAS and similar, it is used to count the number of sign changes to determine the number of roots.
My question is, what to do if the rule reports, say, two sign changes for interval which does not contain any roots?

velinariojepvg 2022-05-09 Answered

True or false: if $a_{n}$ is any decreasing sequence of positive real numbers and $b_{n}$ is any sequence of real numbers converges to $0$ , then $\frac{a_{n}}{b_{n}}$ diverges.

London Ware 2022-05-08 Answered

My problem is the following. I like to know if there exist a sentence true in complex a field but false in a field of positive characteristic.

Azzalictpdv 2022-05-07 Answered

How the false positive value affects accuracy?
$T P (t r u e p o s i t i v e) = 2739$
$T N (t r u e n e g a t i v e) = 103217$
$F P (f a l s e p o s i t i v e) = 43423$
$F N (f a l s e n e g a t i v e) = 5022$
$a c c u r a c y = \frac{T P + T N}{T P + T N + F P + F N}$
In this case the accuracy is $0.68$ . Can I say that I have low accuracy because the value false positive is high? There is any relathion between false positive and the parameters true positive or true negative?

Paula Boyer 2022-05-01 Answered

The latest worldwide virus has an infection rate of $0.1 %$ (that is, $1$ in $1000$ people actually have the virus). The chance that someone who has the virus tests positive is said to be $99 %$ . The chance that someone who does not have the virus tests negative is also said to be $99 %$ . What are the chances that someone who tests positive does not in fact have the virus (a “false positive”)?

bacfrancaiso0j 2022-04-30 Answered

3% of the population has disease X.
A laboratory blood test has
(a) 96% effective at detecting disease X, given that the person actually has it.
(b) 1% “false positive” rate. i.e, a person who does not have disease X has a probability of 0.01 of obtaining a test result implying they have the disease.
What is the probability a person has the disease given that the test result is positive?

Jayla Faulkner 2022-04-07 Answered

A pregnancy test kit is 98.5% accurate for true positive result, i.e. the result is positive when the tester is actually pregnant. If she is not pregnant, however, it may yield a 0.8% false positive. Suppose a woman using this pregnancy kit is 60% at risk of being pregnant.
Not sure about her first test which turned out to be negative, the woman decides to take the test again. This second test, however, turns out to be positive. Assuming the two test are independent, find the probability that she is actually pregnant.
Now she is so confused whether or not she is pregnant. So she take the tests n more times and the results for these n more tests are all positive. Find the minimum value for n so that she can be at least 99.99% sure of pregnancy, assuming all test are independent.

Daphne Haney 2022-04-07 Answered

The prevalence of breast cancer in women over 40 in country X is estimated to be 0.8% (i.e., 8 in every 1,000 women in that age group).
Mammograms test for the presence of breast cancer. A positive result indicates that the disease is present. A negative result indicates that it is not.
The sensitivity of a mammogram test for breast cancer is estimated to be 90%. This is the probability that the mammogram will give a positive result when the person being tested does have breast cancer.
The false positive rate for the mammogram is 7.5%. This is the probability that the mammogram will give a positive test result when the person being tested does not have breast cancer.
All women who test positive (816) in the mammogram are referred for a further, different examination, which however has the same sensitivity and false positive rates as the first test.
What is the probability that a woman referred for this examination and testing positive again, actually does have breast cancer?

Marissa Singh 2022-04-06 Answered

The occurrence of false positives [in some experiment] is 40%
What does this mean? Does it mean that 40% of positives are false? Or 40% of all tested patients are specifically both false and positive? Or say 40% of those that are false are positive?

Karissa Sosa 2022-04-06 Answered

What is the rationale behind ROC curves?
I am not sure how ROC curves work. I see that the X-Axis is the false positive rate while the Y axis is the true positive rate.
1) I don't understand how for a given statistical learning model, you could have the true positive and false positive rate to vary from 0 to
1. Are you changing parameters in the model to make it so?
2) What about true negatives and false negatives? How are these represented in the curve?