Chapter 10: Problem 15
Ann Landers, in her advice column of October 24,1994 (San Luis Obispo Telegram-Tribune), described the reliability of DNA paternity testing as follows: "To get a completely accurate result, you would have to be tested, and so would (the man) and your mother. The test is \(100 \%\) accurate if the man is not the father and \(99.9 \%\) accurate if he is." a. Consider using the results of DNA paternity testing to decide between the following two hypotheses: \(H_{0}:\) a particular man is the father \(H_{a}:\) a particular man is not the father In the context of this problem, describe 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.) b. Based on the information given, what are the values of \(\alpha,\) the probability of a Type I error, and \(\beta,\) the probability of a Type II error? c. Ann Landers also stated, "If the mother is not tested, there is a \(0.8 \%\) chance of a false positive." For the hypotheses given in Part (a), what is the value of \(\beta\) if the decision is based on DNA testing in which the mother is not tested?
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