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Jury trial outcomes. Sometimes, the outcome of a jury trial defies the "commonsense" expectations of the general public (e.g., the 1995 O. J. Simpson verdict and the 2011 Casey Anthony verdict). Such a verdict is more acceptable if we understand that the jury trial of an accused murderer is analogous to the statistical hypothesis-testing process. The null hypothesis in a jury trial is that the accused is innocent. (The status quo hypothesis in the U.S. system of justice is innocence, which is assumed to be true until proven beyond a reasonable doubt.) The alternative hypothesis is guilt, which is accepted only when sufficient evidence exists to establish its truth. If the vote of the jury is unanimous in favor of guilt, the null hypothesis of innocence is rejected and the court concludes that the accused murderer is guilty. Any vote other than a unanimous one for guilt results in a "not guilty" verdict. The court never accepts the null hypothesis; that is, the court never declares the accused "innocent." A "not guilty" verdict (as in the O. J. Simpson case) implies that the court could not find the defendant guilty beyond a reasonable doubt. a. Define Type I and Type II errors in a murder trial. b. Which of the two errors is the more serious? Explain. c. The court does not, in general, know the values of $\alpha$ and $\beta,$ but ideally, both should be small. One of these probabilities is assumed to be smaller than the other in a jury trial. Which one, and why? d. The court system relies on the belief that the value of $\alpha$ is made very small by requiring a unanimous vote before guilt is concluded. Explain why this is so. e. For a jury prejudiced against a guilty verdict as the trial begins, will the value of $\alpha$ increase or decrease? Explain. f. For a jury prejudiced against a guilty verdict as the trial begins, will the value of $\beta$ increase or decrease? Explain.

Name: Problem 20, Chapter 8: Statistics
Uploaded: 2022-01-28T16:20:41-08:00
Duration: 4 min 50 s
Channel: Lucas Finney

Jury trial outcomes. Sometimes, the outcome of a jury trial defies the "commonsense" expectations of the general public (e.g., the 1995 O. J. Simpson verdict and the 2011 Casey Anthony verdict). Such a verdict is more acceptable if we understand that the jury trial of an accused murderer is analogous to the statistical hypothesis-testing process. The null hypothesis in a jury trial is that the accused is innocent. (The status quo hypothesis in the
U.S. system of justice is innocence, which is assumed to be true until proven beyond a reasonable doubt.) The alternative hypothesis is guilt, which is accepted only when sufficient evidence exists to establish its truth. If the vote of the jury is unanimous in favor of guilt, the null hypothesis of innocence is rejected and the court concludes that the accused murderer is guilty. Any vote other than a unanimous one for guilt results in a "not guilty" verdict. The court never accepts the null hypothesis; that is, the court never declares the accused "innocent." A "not guilty" verdict (as in the O. J. Simpson case) implies that the court could not find the defendant guilty beyond a reasonable doubt.
a. Define Type I and Type II errors in a murder trial.
b. Which of the two errors is the more serious? Explain.
c. The court does not, in general, know the values of $\alpha$ and $\beta,$ but ideally, both should be small. One of these probabilities is assumed to be smaller than the other in a jury trial. Which one, and why?
d. The court system relies on the belief that the value of $\alpha$ is made very small by requiring a unanimous vote before guilt is concluded. Explain why this is so.
e. For a jury prejudiced against a guilty verdict as the trial begins, will the value of $\alpha$ increase or decrease? Explain.
f. For a jury prejudiced against a guilty verdict as the trial begins, will the value of $\beta$ increase or decrease? Explain.

Statistics

James T. McClave,… 13th Edition

Chapter 8, Problem 20

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Solved by Expert Lucas Finney

01/28/2022

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This is when the null hypothesis (the accused is innocent) is true, but it is rejected. In other words, an innocent person is found guilty. A Type II error (false negative) occurs when a guilty person is acquitted. This is when the null hypothesis is false, but Show more…

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Jury trial outcomes. Sometimes, the outcome of a jury trial defies the "commonsense" expectations of the general public (e.g., the 1995 O. J. Simpson verdict and the 2011 Casey Anthony verdict). Such a verdict is more acceptable if we understand that the jury trial of an accused murderer is analogous to the statistical hypothesis-testing process. The null hypothesis in a jury trial is that the accused is innocent. (The status quo hypothesis in the U.S. system of justice is innocence, which is assumed to be true until proven beyond a reasonable doubt.) The alternative hypothesis is guilt, which is accepted only when sufficient evidence exists to establish its truth. If the vote of the jury is unanimous in favor of guilt, the null hypothesis of innocence is rejected and the court concludes that the accused murderer is guilty. Any vote other than a unanimous one for guilt results in a "not guilty" verdict. The court never accepts the null hypothesis; that is, the court never declares the accused "innocent." A "not guilty" verdict (as in the O. J. Simpson case) implies that the court could not find the defendant guilty beyond a reasonable doubt. a. Define Type I and Type II errors in a murder trial. b. Which of the two errors is the more serious? Explain. c. The court does not, in general, know the values of $\alpha$ and $\beta,$ but ideally, both should be small. One of these probabilities is assumed to be smaller than the other in a jury trial. Which one, and why? d. The court system relies on the belief that the value of $\alpha$ is made very small by requiring a unanimous vote before guilt is concluded. Explain why this is so. e. For a jury prejudiced against a guilty verdict as the trial begins, will the value of $\alpha$ increase or decrease? Explain. f. For a jury prejudiced against a guilty verdict as the trial begins, will the value of $\beta$ increase or decrease? Explain.

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Key Concepts

Jury Prejudice and Its Impact on Errors

Prejudices held by a jury can bias the decision-making process, potentially altering the error probabilities. A jury predisposed against convicting may inadvertently lower the chance of a Type I error but increase the likelihood of a Type II error, thereby reducing the overall culpability finding even in cases with sufficient evidence.

Jury Unanimity Requirement

The requirement of a unanimous verdict to convict is intended to ensure that the evidence is overwhelmingly convincing. This higher threshold is a procedural safeguard aimed at significantly reducing the probability of a Type I error, meaning it lowers the chance of convicting an innocent person.

Alpha and Beta Error Probabilities

Alpha (?) represents the probability of making a Type I error, while Beta (?) represents the probability of a Type II error. The design of the legal system typically places a stronger emphasis on minimizing ?, thereby reducing the risk of wrongful conviction even if it means accepting a higher chance of a guilty person going free.

Type II Error

A Type II error happens when the null hypothesis is not rejected when the alternative hypothesis is true. In legal terms, this means that a guilty person is acquitted because the evidence was not deemed sufficient to meet the high standard required to convict.

Statistical Hypothesis Testing

This concept involves making decisions about the validity of a claim or hypothesis using evidence and probabilistic reasoning. In the legal context, the process is analogous to determining whether the evidence surpasses a certain threshold of confidence to reject a default position or null hypothesis.

Alternative Hypothesis

The alternative hypothesis is the claim that replaces the null hypothesis when there is enough evidence to support a different conclusion. In a jury trial, this is the assertion that the accused is guilty, and it is accepted only when the evidence meets a high standard of certainty.

Null Hypothesis

In hypothesis testing, the null hypothesis represents the status quo or default state that is assumed to be true until sufficient evidence suggests otherwise. In a legal setting, this corresponds to the presumption of innocence, meaning the accused is assumed innocent unless proven guilty beyond a reasonable doubt.

Type I Error

A Type I error occurs when the null hypothesis is wrongly rejected when it is actually true. In a jury trial context, this error represents convicting an innocent person. Reducing the likelihood of this error is crucial because it undermines the principle of 'innocent until proven guilty'.

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