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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