Question

Medical personnel are required to report suspected cases of child abuse. Because some diseases have symptoms...

Medical personnel are required to report suspected cases of child abuse. Because some diseases have symptoms that mimic those of child abuse, doctors who see a child with these symptoms must decide between two competing hypotheses:

H0: symptoms are due to child abuse H1: symptoms are due to disease

(Although these are not hypotheses about a population characteristic, this problem illustrates the definitions of Type I and Type II errors.) The article “Blurred Line Between Illness, Abuse Creates Problem for Authorities” (Macon Telegraph, February 28, 2000) included the following quote from a doctor in Atlanta regarding the consequences of making an incorrect decision: “If it’s disease, the worst you have is an angry family. If it is abuse, the other kids (in the family) are in deadly danger.”

(a) For the given hypotheses, describe Type I and Type II errors.

(b) Based on the quote regarding consequences of the two kinds of error, which type of error does the doctor quoted consider more serious? Explain.

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