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 reject ho when it is true. here is conclude guily when he is actually not. type II error is failure to reject ho when it is false. here i conclude innocent when he is actually guilty.

b) Probabiltiy of type II error is more serious as compared to type I error. concluding and punishing a innocent is LESS serious as comrped to case when a guily person is proved innocent. he can form harm and crime in the city.

c) The probability of making Type II error should be smaller. since type II error is more serious in this case, i want to control type II error. that is indirectly controlling power.

d) deciding the level of signiicance, alpha, implies that i am (1-alpha)% confident about my reuslts. If the probability of observed sample outcome is lower than alpha level, then null hypothesis is rejected.

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