STA 412-Hand-in Homework #3-Fall 2018/Sections 2.6.2.10 Due Friday September 21
ID: 3071514 • Letter: S
Question
STA 412-Hand-in Homework #3-Fall 2018/Sections 2.6.2.10 Due Friday September 21 Page 2 of a hypothetical population of 10,000 adults, 5% have diabetes. Suppose every person in the population receives a blood sugar test, which is used to screen for diabetes. The results are in the table below: s Patient Actually Diabetic? No (D) 1,900 7,600 9,500 Yes (D) Total 2,250 7.750 10,000 Result of the Positive (BS)350 Blood Sugar Negative (BS) (BS) Test 150 500 Total The sensitivity of a test is the probability that, when a person has the disease (read: GIVEN the person has the disease), the test for the disease will come back positive for that person. Find the sensitivity for the Blood Sugar test for this population. a. b. The specificity of a test is the probability that, when a person does not have the disease (read: GIVEN the person does not have the disease), the test for the disease will come back negative for that person. Find the specificity for the Blood Sugar test for this population. c. The false positive rate of a test is the probability that, when a person does not have the disease, the test for the disease will nevertheless come back positive for that person. Find the false positive rate for the Blood Sugar test for this population d. The false negative rate of a test is the probability that, when a person has the disease, the test for the disease will nevertheless come back negative for that person. Find the false negative rate for the Blood Sugar test for this population. e. The positive predictive value (PPM of a test is the probability that, when the test comes back positive, that the person has the disease. Find the positive predictive value for the Blood Sugar test for this population.Explanation / Answer
a)
sensitivity =P(positive test|have disease)=350/500=0.7
b)
specificity =P(negative test|not have disease)=7600/9500=0.8
c)
false posiive rate =1-speciificity =1-0.8 =0.2
d)
false negative rate =1-sensitivity =1-0.7 =0.3
e)
positive predictive value =true positive/total posiitve =350/2250 =0.15556
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