Criminal trials A hypothesis test can be thought of like a criminal trial. When a person is charged with a crime, this person, the defendant, is either innocent or guilty. We can think of the null hypothesis as the defendant is innocent and the alternative as the defendant is guilty. In the trial the prosecution gives evidence to try to show the defendant is guilty. The jury then makes a decision of guilty or not guilty. Hopefully they make the correct decision. If not, there are two types of decision errors that could be made.

(a) In this scenario, describe what it means for the null hypothesis to be rejected when, in fact, it is true.

Rejecting a true null hypothesis is finding an innocent person guilty.

Rejecting a true null hypothesis is finding a guilty person not guilty.

(b) In this scenario, describe what it means if the null hypothesis is not rejected when, in fact, it is false.

Not rejecting a false null hypothesis is finding an innocent person guilty.

Not rejecting a false null hypothesis is finding a guilty person not guilty.

(c) Our judicial system is supposed to be set up to make the likelihood of making one of these as small as possible. Which one of these decision errors is that, the one described in part (a) or the one described in part (b)?

Our judicial system is supposed to be set up to make it difficult to find an innocent person guilty, the error described in part (a).

Our judicial system is supposed to be set up to make it difficult to find an innocent person guilty, the error described in part (b).

Our judicial system is supposed to be set up to make it difficult to find a guilty person not guilty, the error described in part (a).

Our judicial system is supposed to be set up to make it difficult to find a guilty person not guilty, the error described in part (b).