Chapter 7: Q17E (page 399)

Jury trial outcomes. Sometimes, the outcome of a jury trial defies the “common sense” 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 Casey Anthony 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 α and β ; 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 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 ofα increase or decrease? Explain.
f. For a jury prejudiced against a guilty verdict as the trial begins, will the value of β increase or decrease? Explain

Short Answer

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a. Type 1 error occurs when a jury finds a defendant guilty of murder despite the fact that the defendant is innocent in murder trial. Type 2 error occurs if the accused is found guilty of murder but is mistakenly deemed not guilty of in the murder trial.

b. Type 1 error is more serious.

c. The type 1 error is assumed to be smaller than type 2 error in the jury trial.

d. Theα is minimized because a jury member may each have their own level of error.

e. The β will decrease.

Step by step solution

Type 1 error and Type 2 error

a. *Type 1 error

It implies rejecting the null hypothesis, when actually it is true

Type 1 error occurs when a jury finds a defendant guilty of murder despite the fact that the defendant is innocent in the murder trial.

*Type 2 error

It implies accepting the null hypothesis, when actually it is false.

Type 2 error occurs if the accused is found guilty of murder but is mistakenly deemed not guilty in the murder trial.

Finding which of the two errors is the more serious

b. Type 1 error is more serious as the defendant is found guilty of murder when, in fact they are not.

Finding which of the probabilities is smaller than the other in the jury trial

c.Let α be the type 1 error.

Let β be the type 2 error.

We try to minimize the type 1 error as the jury is unanimous in favor of guilt.

Therefore, the type 1 error is assumed to be smaller than type 2 error in a jury trial.

Explaining part d. of the question

d. The value of α is minimized because jury members each have their own level of error in their ability to differentiate between the guilt and innocence of the accused. Hence the minimum error occurs.

Explaining part e. of the question

e. Early in the trial, if the jury is prejudiced against the guilty verdict, It is likely that the accused be not guilty of murder. The probability of him being falsely convicted will decrease. Hence, the value of αwill decrease.

Explaining part f. of the question

f. Early in the trial, the jury was biased against the guilty verdict. It is likely that the defendant is actually guilty of murder. It increases the likelihood that he will be wrongfully convicted. Hence, the value of β will increase.