Please answer any questions that have a blank or filled box, thanks!! 1). The ac
ID: 3044294 • Letter: P
Question
Please answer any questions that have a blank or filled box, thanks!!
1). The accompanying table gives the results of a screening test for a disease. Estimate the sensitivity and specificity of the test.
Sensitivity %
Specificity %
Has disease Does not have disease
Test positive 15 12
Test negative 5 68
2).
Suppose a test for a disease has a sensitivity of 95% and a specificity of 60%. Further suppose that in a certain country with a population of 1,000,000, 20% of the population has the disease.
Fill in the accompanying table.
Has disease Does not have disease Totals
Test positive
Test negative
Totals
3).
A certain genetic condition affects 5% of the population in a city of 10,000. Suppose there is a test for the condition that has an error rate of 1% (i.e., 1% false negatives and 1% false positives).
Fill in the table below.
Has condition Does not have condition Totals
Test positive
Test negative
Totals
4).
Here is a scenario that came up in the nationally syndicated column called "Ask Marilyn" in Parade Magazine. Suppose a certain drug test is 95% accurate, meaning that if a person is a user, the result is positive 95% of the time, and if she or he isn't a user, it's negative 95% of the time. Assume that 20% of all people are drug users.
Assume that the population is 10,000, and fill in the accompanying table.
Drug user Not a drug user Totals
Test positive
Test negative
Totals
5).
A certain genetic condition affects 5% of the population in a city of 10,000. Suppose there is a test for the condition that has an error rate of 1% (i.e., 1% false negatives and 1% false positives).
Consider the values that would complete the table below.
Has condition Does not have condition Totals
Test positive
Test negative
Totals
What is the probability (as a percentage) that a person does not have the condition if he or she tests negative? (Round your answer to once decimal place.)
%
6).
Suppose that a certain HIV test has both a sensitivity and specificity of 99.9%. This test is applied to a population of 1,000,000 people.
Suppose that 1% of the population is actually infected with HIV.
(a) Calculate the PPV. Suggestion: First make a table as seen below. (Round your answer to one decimal place.)
Has disease Does not have disease Totals
Test positive
Test negative
Totals
(b) Calculate the NPV. (Round your answer to three decimal places.)
(c) How many people will test positive who are, in fact, disease-free?
7).
This question refers to the table below.
Has TB Does not have TB
Test positive 476 35
Test negative 236 343
9).
Bayes's theorem on conditional probabilities states that, if P(B) is not 0, then
P(A given B) =
P(B given A) × P(A)
P(B)
.
Leave your answers as fractions.
Mary bakes 6 chocolate chip cookies and 10 peanut butter cookies. Bill bakes 5 chocolate chip cookies and 10 peanut butter cookies. The 31 cookies are put together and offered on a single plate. I pick a cookie at random from the plate.
(a) What is the probability that the cookie is chocolate chip?
(b) What is the probability that Mary baked the cookie?
(c) What is the probability that the cookie is chocolate chip given that Mary baked it?
(d) Use Bayes's theorem to calculate the probability that the cookie is baked by Mary given that it is chocolate chip. In this situation, Bayes's theorem tells us that
P(Mary given Chocolate) =
P(Chocolate given Mary) × P(Mary)
P(Chocolate)
(e) Calculate without using Bayes's theorem the probability that the cookie is baked by Mary given that it is chocolate chip. Suggestion: How many of the chocolate chip cookies were baked by Mary?
10).
Bayes's theorem on conditional probabilities states that, if P(B) is not 0, then
P(A given B) =
P(B given A) × P(A)
P(B)
.
Yesterday car lot Alpha had two Toyotas and one Chevrolet for sale. Car lot Beta had three Toyotas and five Chevrolets for sale. This morning Alan bought a car, choosing one of the two lots at random and then choosing a car at random from that lot. Leave your answers as fractions.
(a) What is the probability that Alan bought from Alpha?
(b) If Alan bought from Alpha, what is the probability he bought a Toyota?
(c) If Alan bought from Beta, what is the probability he bought a Toyota?
(d) It can be shown that the probability that Alan bought a Toyota is 25/48. What is the probability Alan bought from Alpha given that he bought a Toyota? Note: In this situation, Bayes's theorem says
P(Alpha given Toyota) =
P(Toyota given Alpha) × P(Alpha)
P(Toyota)
Find the probability that a person tests positive given that the person does not have the disease. (Round your answer to one decimal place.)
Explanation / Answer
Sensitivity = TP/(TP+FN)= 15/(15+5)=15/20=0.75
Specificity= TN/(TN+FP)=68/(68+12)=0.85
2)
Suppose a test for a disease has a sensitivity of 95% and a specificity of 60%. Further suppose that in a certain country with a population of 1,000,000, 20% of the population has the disease.
Fill in the accompanying table.
Has disease Does not have disease Totals
Test positive 0.19 0.32 0.51
Test negative 0.01 0.48 0.49
Totals 0.2 0.80 1
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