Medical personnel are required to report suspected cases of child abuse. Because
ID: 3310851 • Letter: M
Question
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.
(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.) An article 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.
A Type I error is coming to the conclusion that the symptoms are due to ---Select--- child abuse disease when in fact the symptoms are due to ---Select--- child abuse disease .
A Type II error is coming to the conclusion that the symptoms are due to ---Select--- child abuse disease when in fact the symptoms are due to ---Select--- child abuse disease .
(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.
The doctor considers the presence of ---Select--- child abuse disease more serious than the presence of ---Select--- child abuse disease . Thus, according to the doctor, undetected ---Select--- child abuse disease is more serious than undetected ---Select--- child abuse disease , and a ---Select--- Type I Type II error is the more serious.
H0: symptoms are due to child abuse Ha: symptoms are due to diseaseExplanation / Answer
a) A Type I error is coming to the conclusion that the symptoms are due to disease when in fact the symptoms are due to child abuse
A Type II error is coming to the conclusion that the symptoms are due to child abuse when in fact the symptoms are due to disease
b) The doctor considers the presence of disease more serious than the presence of child abuse.
Thus, according to the doctor, undetected disease is more serious than undetected child abuse and a Type II error is the more serious.