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: H0: a particular man is the father Ha: 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 a, the probability of a Type I error, and b, 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 b if the decision is based on DNA testing in which the mother is not tested?