00:01
Hello students, in this question by using the given information, we have to calculate the negative predictive value of the test.
00:07
So let d is for diseases and t is for test positive.
00:19
Test positive.
00:23
Then we have given that a test group of 1000 people is comprised of 200 people known to have the disease and 800 people known to be free of the disease.
00:34
So by using that we can compute probability of a d is equal to 200 divided by 1000 which is equal to 0 .2.
00:43
Also given that a diagnostic test is 92 % sensitive and 94 % specific.
00:49
So therefore probability of d intersection t that is equal to probability of now this probability is nothing but probability of d and t and this we can write in terms of the conditional probability that is probability of t given d into probability of d and that is equal to now probability of t given d is the 92 % sensitive that means 0 .92 into probability of d is 0 .2.
01:22
So we will get probability of d and t is equal to 0 .184.
01:28
Similarly we can compute probability of d complement intersection t complement which is equal to probability of t complement given d complement into probability of d complement which is equal to 0 .94 which is the specificity into 0 .8 which is the probability of d complement which we can compute as probability of d complement is equal to 1 minus probability of d.
01:59
So now this is equal to 0 .752 and now we can complete this table...