Chapter 10.2, Problem 14E

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

H_a: symptoms are due to disease

(Although these are not hypotheses about a population characteristic, this exercise 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.”

1. a. For the given hypotheses, describe Type I and Type II errors.
2. 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.