A jury trial of an accused murderer is analogous to the statistical hypothesis-t

Question

A jury trial of an accused murderer is analogous to the statistical hypothesis-testing process. The null hypothesis in a jury trial is that the accursed 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 guilty, 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 otehr 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 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 more serious? Explain.

c. Let and denote the probabilities of making type I and type II errors, respectively. The court does not know the values of and in general, but ideally both should be small. One of these probabilities is assumed to be smaller than the other in a jury trial. Which one should be smaller? 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 of increase or decrease?

f. For a jury prejudiced against a guilty verdict as the trial begins, will the value of increase or decrease?

Explanation / Answer

a) Type I error is when the true null hypothesis that is accused is innocent is rejected (concluding innocent person to be guilty) and Type II error is failure to reject a false null hypothesis that is insufficient evidence to conclude that accused is guilt (accused guilty person is proved non-guilty).

c) The probability of making Type II error should be smaller. The probailities of two types of errors are inversely related, and as one decreases the other increases. Minimizing two type of errors in on etest is not possible. Ideally aim of researcher is to reject null hypothesis. Therefore, probbaility of the failure to reject a false null hypothesis should be minimized.

d) When the court decides on alpha level, it actually defines an unlikely sample outcome. If the probability of observed sample outcome is lower than alpha level, then null hypothesis is rejected.

f) Beta will remain

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