When designing a hypothesis test, one of the first decisions that needs to be ma

Question

When designing a hypothesis test, one of the first decisions that needs to be made is which hypothesis to assign to H0 and which hypothesis to assign to Ha . One criterion that was discussed was to assign the hypothesis to H0 for which the consequences of a type I error are worse than the consequences of a type II error .

Consider the following hypothetical scenario. Suppose that Michael is convicted of a crime. If the judge determines that Michael is guilty of the crime, then Michael will be sent to prison. In this scenario, there are two possible hypothesis tests that can be considered.

Hypothesis Test A : H0: Michael is guilty versus Ha: Michael is not guilty

Hypothesis Test B : H0: Michael is not guilty versus Ha: Michael is guilty

In your opinion, for which of these two hypothesis tests (Test A or Test B) are the consequences of a type I error worse than the consequences of a type II error ?

Be sure to justify your decision, and to explain the practical significance (in terms of Michael being sent to prison) of the hypothesis test you have chosen.

Explanation / Answer

For hypothesis A rejecting the null hypothesis when he is guilty is not bad, so Type-I error is good

For hypothesis B rejecting the null hypothesis when he is not guilty is not good as in that case not guilty is punished. Hence for hypothesis B, Type-I error is worse than Type-II error.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.