A new non-invasive screening test is proposed that is claimed to be able to identify patients with impaired glucose tolerance based on a battery of questions related to health behaviors. The new test is given to 75 patients. Based on each patient's responses to the questions they are classified as positive or negative for impaired glucose tolerance. Each patient also submits a blood sample and their glucose tolerance status is determined. The results are tabulated below.
|
Screening Test
|
Impaired Glucose Tolerance
|
Not Impaired
|
|
Positive
|
17
|
13
|
|
Negative
|
8
|
37
|
a) What is the sensitivity of the screening test?
b) What is the false positive fraction of the screening test?