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: $H_{0}:$ 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." 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.
Added by Susan P.
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Type I error occurs when we reject the null hypothesis ($H_{0}$) when it is actually true. In this case, it means that we conclude the symptoms are due to disease (rejecting child abuse) when they are actually due to child abuse. Type II error occurs when we fail Show more…
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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: $H_{0}$ : 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." 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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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 HA : Symptoms are not due to child abuse During an interview, an Atlanta doctor stated, "If it's actually a disease, the worst you have is an angry family. If it is abuse, the kids in the family are in deadly danger." What is a Type II error in the context of this problem? A Type II error indicates doctor rejected Ho, and the doctor is claiming the symptoms are NOT due to child abuse but they actually are due to child abuse. The family is not angry but the kids are in danger. A Type II error indicates the doctor failed to reject Ho, and the doctor is claiming the symptoms are due to child abuse but they actually are not due to child abuse. The family is very angry at the doctor but the kids are not in danger. A Type II error indicates doctor failed to reject Ho, and the doctor is claiming the symptoms are NOT due to child abuse but they actually are due to child abuse. The family is not angry but the kids are in danger. A Type II error indicates the doctor rejected Ho, and the doctor is claiming the symptoms are due to child abuse but they actually are not due to child abuse. The family is very angry at the doctor but the kids are not in danger.
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