Question

2. A study was conducted to investigate a new procedure for detecting renal disease in patients with hypertension. Using the new procedure, experimenters screened a random sample of 250 hypertensive patients. Then the presence or absence of renal disease was determined by another method. The obtained are shown in the following table Disease Detected Disease Not Detected Disease Absent 17 202 Disease Present 25 (a) [1 mark] Find the false positive rate for the new procedure. (b) [1 mark] Find the false negative rate for the new procedure. (c) [1 mark] Are the events "has the disease" and "disease not detected independent? (Show a calculation!) (d) [1 mark] Are the events "has the disease" and "disease not detected" mutually exclusive? Explain

Answer 1

	absent	present	total
disease +	17	25	42
no disease -	202	6	208
total	219	31	250

a) P(false positve rate) = 17/250 =               0.068  
                  
b) P(false negative) = 6/250=               0.024  
                  
c)to be independent events                  
P(has disease and disease not detected) = P(has disease)*P(disease not detected)                  
P(has disease and disease not detected) = 6/250               0.024  
                  
P(has disease)*P(disease not detected) = 31/250*208/250=               0.103168  
                  
since, P(has disease and disease not detected) ╪ P(has disease)*P(disease not detected)                  
                  
so, events are not indepdnet                  
                  
d) events to be mutually exclusive, P(A and B) must be 0                  
but here, P(has disease and disease not detected) ╪0                  
so, events are not mutually exclusive