Q1. Suppose two doctors, A and B, test all patients coming into a clinic for syphilis. Let events A+ = (doctor A makes a positive diagnosis) and B+ = (doctor B makes a positive diagnosis}. Suppose doctor A diagnoses 10% of all patients as positive, doctor B diagnoses 17% of all patients as positive, and both doctors diagnose 8% of all patients as positive.
a. Are the events A+, B+ independent?
Suppose a patient is referred for further lab tests if either doctor A or B makes a positive diagnosis.
b. What is the probability that a patient will be referred for further lab test?
Q2. A certain virus infects five in every 400 people. A test used to detect the virus in a person is positive 85% of the time when the person has the virus and 8% of the time when the person does not have the virus. Let A be the event "the person is infected" and B be the event "the person tests positive."
a. Using Bayes' Theorem, when a person tests positive, determine the probability that the person is infected.
b. Using Bayes' Theorem, when a person tests negative, determine the probability that a person is not infected.
Q3. Skinfold thickness over the triceps muscle in the arm is an anthropometric measure that varies with states of health. Table 1 below lists skinfold measurement at the midpoint of the triceps in eight men with chronic lung disease and nine comparably aged controls.
a. Compare the groups with side-by-side stem-plots.
b. Calculate group means, medians, variances, and standard deviations.
c. Draw a boxplot for each data, and determine any outlier?
Table 1 -
|
Chronic lung disease:
|
9.1
|
10.9
|
11.4
|
15.3
|
25.4
|
12.5
|
20.7
|
18.2
|
|
|
Controls:
|
31.4
|
39.0
|
23.0
|
18.8
|
24.7
|
32.8
|
25.7
|
36.4
|
19.2
|
Q4. The probability that a patient is allergic to Tylenol is 0.30. Suppose this drug is administered to four patients:
a. Find the probability that all four of them are allergic to it?
b. Find the probability that at least one of them is not allergic to it?
Q5. The table below shows how the risk ratio was calculated in a study examining the risk of wound infections when an incidental appendectomy was done during a staging laparotomy for Hodgkin's disease.
a. Calculated the Relative Risk and give an Interpretation of the result?
|
Have Incidental Appendectomy?
|
Wound Infection
|
No Wound Infection
|
|
Yes
|
9
|
195
|
|
No
|
3
|
85
|
Q6- A scientist designed a medical test for a certain disease. Among 100 patients who have the disease, the test will show the presence of the disease in 97 cases out of 100, and will fail to show the presence of the disease in the remaining 3 cases out of 100. Among those who do not have the disease, the test will erroneously show the presence of the disease in 4 cases out of 100, and will show there is no disease in the remaining 96 cases out of 100.
a. What is the probability that a patient who tested positive on this test actually has the disease, if it is estimated that 20% of the population has the disease?
b. What is the probability that a patient who tested negative on this test actually does not have the disease, if it is estimated that 4% of the population has the disease?