Question
In: Math
A diagnostic test for a certain disease is applied to n individuals known to not have...
A diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results.
(a) Derive the maximum likelihood estimator of p.
If n = 20 and x = 7, what is the estimate?
(b) Is the estimator of part (a) unbiased?
(c) If n = 20 and x = 7, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.)
Solutions
milcah answered 2 years agoRelated Solutions
Consider a diagnostic test for a hypothetical disease based on measuring the amount of a certain...
Consider a diagnostic test for a hypothetical disease based on
measuring the amount of a
certain biomarker present in blood. High levels of the biomarker
are often found in individuals
with the disease, but a number of non-disease conditions can
also cause high levels
of the biomarker. Individuals without the disease have biomarker
levels that are normally
distributed with mean 1.6 ng/mL (nanograms per milliliter of
blood), and standard deviation
0.50 ng/mL. Individuals with the disease have biomarker levels
that...
Consider a diagnostic test for a hypothetical disease based on measuring the amount of a certain...
Consider a diagnostic test for a hypothetical disease based on
measuring the amount of a
certain biomarker present in blood. High levels of the biomarker
are often found in individuals
with the disease, but a number of non-disease conditions can
also cause high levels
of the biomarker. Individuals without the disease have biomarker
levels that are normally
distributed with mean 1.6 ng/mL (nanograms per milliliter of
blood), and standard deviation
0.50 ng/mL. Individuals with the disease have biomarker levels
that...
Consider a diagnostic test for a hypothetical disease based on measuring the amount of a certain...
Consider a diagnostic test for a hypothetical disease based on
measuring the amount of a certain biomarker present in blood. High
levels of the biomarker are often found in individuals with the
disease, but a number of non-disease conditions can also cause high
levels of the biomarker. Individuals without the disease have
biomarker levels that are normally distributed with mean 1.6 ng/mL
(nanograms per milliliter of blood), and standard deviation 0.50
ng/mL. Individuals with the disease have biomarker levels that...
Consider a diagnostic test for a hypothetical disease based on measuring the amount of a certain...
Consider a diagnostic test for a hypothetical disease based on
measuring the amount of a certain biomarker present in blood. High
levels of the biomarker are often found in individuals with the
disease, but a number of non-disease conditions can also cause high
levels of the biomarker. Individuals without the disease have
biomarker levels that are normally distributed with mean 1.6 ng/mL
(nanograms per milliliter of blood), and standard deviation 0.50
ng/mL. Individuals with the disease have biomarker levels that...
Scores on a certain IQ test are known to have a mean of 100. A random...
Scores on a certain IQ test are known to have a mean of 100. A
random sample of 60 students attend a series of coaching classes
before taking the test. Let m be the population mean IQ score that
would occur if every student took the coaching classes. The classes
are successful if m > 100. A test is made of the hypotheses H0:
m = 100 vs H1: m > 100.
Consider three possible conclusions:
The classes are successful....
In a certain risk group, individuals are tested for a certain disease S. A person who...
In a certain risk group, individuals are tested for a certain
disease S. A person who has the disease gets the correct diagnosis
with probability 0.99, whereas a person who does not suffer from S
gets the correct diagnosis with probability 0.95. Furthermore, it
is known that 6% of the individuals in the group get the diagnosis
“suffer from S”. Determine a) the proportion of individuals in the
group who suffer from S, and b) the probability that a person...
A certain IQ test is known to have a population mean of 100 and standard deviation...
A certain IQ test is known to have a population mean of 100 and
standard deviation of 15 in the general population. You want to
test whether psychology majors have a different average IQ than the
population as a whole. Assume the variance of IQ is the same for
Psych majors as it is in the general population.
Suppose that Psychology majors actually have an average IQ of
108. If you do a 2-tailed test at α= .05 with a...
A diagnostic test for a disease has a true positive rate of 98% and a true...
A diagnostic test for a disease has a true positive rate of 98%
and a true negative rateof 94%. Suppose the overall disease rate in
the population is 1%. That is,•Pr(Positive Test|Patient has
Disease) = 0.98,•Pr(Negative Test|Patient does NOT have Disease) =
0.94,•Pr(Patient has Disease) = 0.01.a) What is the probability of
a patient without the disease testing positive? b) Find the
probability that a patient has the disease given that they tested
positive.That is, findPr(Patient has Disease|Positive Test).
A diagnostic test either provides a + result (has the disease) or - result (does not...
A diagnostic test either provides a + result (has the disease)
or - result (does not have the disease). 5% of the population has
the disease. For a patient with the disease, 75% will test (+)/ 25%
will test (-). For a patient that does not have the disease, 15 %
will test (+)/ 85% will test (-).
Part A) If everyone in the population is tested, what proportion
of the test results will be positive?
Part B) For a...
A diagnostic test has a probability of 92% of giving a positive result when applied to...
A diagnostic test has a probability of 92% of giving a positive
result when applied to a person suffering from a certain disease.
The test has a probability of 5% of giving a false positive when
applied to a non-sufferer. If 6% of the population suffer from the
disease, what is the probability of a positive test result?
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Year Cash Flow 0 −$9,700 1 5,800 2 2,500 3 3,400 &nb
- In a two – story building, an exterior column is to be designed for a service...
- Explain the use of neural networking modeling in predictive analytics. Discuss a real-life example of where...
- Boarder line and antisocial disorder are perhaps the most research personality disorder.What are the most common...
- Read at least 2 academically reviewed articles and Write an annotated bibliography paper on Master Budgeting
- Why normalization and referential integrity are important principles when designing relational databases?
- Respond to the following in a minimum of 175 words: Discuss what elements should be present...
ADVERTISEMENT