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March 11th, 2011, 09:15 PM  #1 
Newbie Joined: Mar 2011 Posts: 3 Thanks: 0  Challenging Probability and Statistics Questions!
It is known that 5% of the members of a population have disease A, which can be discovered by a blood test. Suppose that N ( a large no.) people are to be tested This can be done in 2 ways : 1. Each person is tested separately , or 2. the blood samples of k people are pooled together and analyzed. ( Assume that N =nk , with n an integer) If the test is ve , all of them are healthy ( that is , just this 1 test is neeeded) if the test is +ve , each of the k persons must be tested separately ( that is , a total of k+1 tests are needed) Questions: a) For the fixed k, what is the expected no. the tests needed in option 2. b) Find the k that will minimize the expected no. of tests in option 2. c) If k is selected as in part b, on the average how many tests does option 2 save in comparison with option1? 
March 12th, 2011, 02:23 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Re: Challenging Probability and Statistics Questions! Quote:
There is something wrong with the problem statement for b, since k=1 is the obvious answer, but it seems wrong for the underlying problem.  
March 13th, 2011, 07:44 AM  #3 
Newbie Joined: Mar 2011 Posts: 3 Thanks: 0  Re: Challenging Probability and Statistics Questions!
for question (a), the answer given is assume the number of expected no. of test for population which means we need to use N=nk. for the number of people in sample k have disease A is (k * (10.95^k)) is it? the number of test is k + 1, so is 1+(k * (10.95^k))? 

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