Sarah just got a test result back after giving blood. The test result suggested
ID: 3227191 • Letter: S
Question
Sarah just got a test result back after giving blood. The test result suggested that she has a rare disease.
It is known that only 2% of the US Adult Population has this disease.
The test Sarah took is not very accurate and in fact the test returns a false positive (test is positive giventhe patient does not have the disease) 10% of the time for patients that do not have the disease.
The test also returns a false negative (a negative test result given the patient has the disease) 5% of the time on patients who do have the disease.
Answer The following probability question using at least 4 decimals.
HINT: the last 2 statement I provide conditional probabilities.
What is the probability a randomly selected Adult has the Disease and Has a Negative Test? (This is a joint probability. Both events must happen here.)
QUESTION 2
Sarah just got a test result back after giving blood. The test result suggested that she has a rare disease.
It is known that only 2% of the US Adult Population has this disease.
The test Sarah took is not very accurate and in fact the test returns a false positive (test is positive giventhe patient does not have the disease) 10% of the time for patients that do not have the disease.
The test also returns a false negative (a negative test result given the patient has the disease) 5% of the time on patients who do have the disease.
Answer The following probability question using at least 4 decimals.
HINT: the last 2 statement I provide conditional probabilities.
What is the probability a randomly selected Adult does not have the Disease and Has a Postive Test? (This is a joint probability. Both events must happen here.)
QUESTION 3
Sarah just got a test result back after giving blood. The test result suggested that she has a rare disease.
It is known that only 2% of the US Adult Population has this disease.
The test Sarah took is not very accurate and in fact the test returns a false positive (test is positive giventhe patient does not have the disease) 10% of the time for patients that do not have the disease.
The test also returns a false negative (a negative test result given the patient has the disease) 5% of the time on patients who do have the disease.
Answer The following probability question using at least 4 decimals.
HINT: the last 2 statement I provide conditional probabilities.
What is the probability a randomly selected Adult Has a Postive Test?
QUESTION 4
Sarah just got a test result back after giving blood. The test result suggested that she has a rare disease.
It is known that only 2% of the US Adult Population has this disease.
The test Sarah took is not very accurate and in fact the test returns a false positive (test is positive giventhe patient does not have the disease) 10% of the time for patients that do not have the disease.
The test also returns a false negative (a negative test result given the patient has the disease) 5% of the time on patients who do have the disease.
Answer The following probability question using at least 4 decimals.
HINT: the last 2 statement I provide conditional probabilities.
What is the probability Sarah actually has the Disease Given the information that She knows she had a postive test result?
QUESTION 5
We have a dataset with one numerical response variable (y) and two numerical explanatory variables (x1 and x2). Here assume the relationship between x1 and the mean response Y depends on the level of x2. Select the correct population model below.
y=0+1x1+
y=0+1x1+
=b0+b1x1+b2x2
=b0+b1x1+b2x2 + bxx1x2
QUESTION 6
We have a dataset with one numerical response variable (y) and two numerical explanatory variables (x1 and x2). Here assume the relationship between x1 and the mean response Y does not depend on the level of x2. Select the correct estimated model below.
y=0+1x1+
y=0+1x1+
=b0+b1x1+b2x2
=b0+b1x1+b2x2 + bxx1x2
QUESTION 7
We have a dataset with one numerical response variable (y) and two numerical explanatory variables (x1 and x2). Here assume the relationship between x1 and the mean response Y does not depend on the level of x2. Select the best interpretation for the population coefficient for the variable x2.
2 is the interpreted as the change in the mean response when x2 increases by one unit regardless of x1.
2 is the interpreted as the change in the predicted response when x1 and x2 increases by one unit.
B2 is interpreted as the chage in the mean response when x2 increases by one units assuming x1 does not change
B2 is the interpreted as the change in the predicted response when x2 increases by one units assuming x1 does not change
y=0+1x1+
y=0+1x1+
=b0+b1x1+b2x2
=b0+b1x1+b2x2 + bxx1x2
Explanation / Answer
(1) Probability = 0.1/100 = 0.001
(2) Probability = 9.8/100 = 0.098
(3) Probability = 11.7/100 = 0.117
(4) Probability = P(Disease and Test +) /P(Test +) = (1.9/100)/(11.7/100) = 0.1624
Test + Test - Total Disease 2 - 0.1 = 1.9 5% of 2 = 0.1 2 No Disease 10% of 98 = 9.8 98 - 9.8 = 88.2 100 - 2 = 98 Total 11.7 88.3 100Related Questions
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