Question

You are selected for jury duty where you will take part in deciding, based on sufficient concrete evidence, whether a defendant is guilty of a serious crime.

In your own words, while applying the concept, logic, and steps of hypothesis testing, answer the following questions and provide one clear reason why for each question:

What is the correct decision for the jury to make in this case?

How often would you want the jury to make this decision?

What is the incorrect decision for the jury to make in this case?

How often would you want the jury to make this decision?

Which decision will do the most harm for the community at large?

Answer 1

As we know that for the hypothesis testing we have to assume two hypothesis i.e null hypothesis and alternative hypothesis .

• Null hypothesis: The defendant is not guilty.

Alternative hypothesis: The defendant is guilty

Then,we have to take a certain test that is defendant is guilty or not on the basis of reasonable doubt or evidence.

Test Statistic: X = number of jurors who vote guilty. (Never 100% certain . . . beyond a reasonable doubt.)

• Two possible jury decisions: a) Reject the null hypothesis: Find the defendant guilty. b) Do not reject the null hypothesis: Find the defendant not guilty.

The jury often want to make decision is to find guilty person guilty and whether not guilty is not guilty on the basis of certain evidence regarding that.

•There is two type of error finding in such type of case.

Two types of possible errors: a) Type 1 or Type I: Reject the null hypothesis but it is true. The jury finds the defendant guilty when he actually isn’t. b) Type 2 or Type II: Do not reject the null hypothesis but it is false. The defendant is guilty; but the jury finds him not guilty.

• when the defendant is not guilty but is proven guilty by the jury decision .This will cause most harm for the community at a large.