How accurate are DNA paternity tests? By comparing the DNA or the baby and the D
ID: 3370793 • Letter: H
Question
How accurate are DNA paternity tests? By comparing the DNA or the baby and the DNA of a man that is being tested, one maker of DNA paternity tests claims that their test is 100% accurate if the man is not the father and 99.99% accurate if the man is the father t (a) Conslder using the result of this DNA paternity test to declde between the following two hypotheses Ho: A partlcular man is not the father H: A partcular man is the father. In the context of thls problem, descrbe Type I and Type II errors. (Although these are not hypotheses about a population characteristic, this exercise Illustrates the definitions of Type I and Type II errors.) A Type I error is coming to the conclusion that a particular man is A Type II error is coming to the conclusion that a particular man is notthe father when, In fact, he is Based on the information given, what are the values of ?, the probability of a Type 1 error, and ?, the probability of a Type II error? ., the father when, in fact, he l is not the father. the father (b)Explanation / Answer
(b)
alpha = Probability of type I error = Pr ( Rejecting null hypo. when it is actually true)
= Pr ( Conclude that the man is father when man is actually not the father)
Note that the test is 100% accurate if the man is not the father. So aplha = 0.
beta = Probability of type II error = Pr ( Accepting null hypo. when it is actually False)
= Pr ( Conclude that the man is not father when man is actually the father)
Note that it is given that the test is 99.99% accurate if man is father. So beta = 1-0.9999 = 0.0001
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