Question

A prisoner on trial for a felony is presumed innocent until proven guilty. (That is, innocent is the null hypothesis.) Which of the following represents the risk involved in making a Type II error?

a. The prisoner is actually guilty and the jury sends him to jail.

b. The prisoner is actually innocent and the jury sends him to jail.

c. The prisoner is actually innocent and the jury sets him free.

d. The prisoner is actually guilty and the jury sets him free.

e. The prisoner is sent to jail.

Answer 1

Option D) The prisoner is actually guilty and the jury sets him free.

Explanation:

We are given the following in the question:

Null Hypothesis:

The null hypothesis states that the prisoner is innocent

Alternate Hypothesis:

The alternate hypothesis states that the prisoner is guilty and not innocent.

Type II error:

It is the type error made when we fail to reject the ll hypothesis when it is actually false.

That is we accept a false null hypothesis.

Thus a type II error in the above scenario will be to accept that the prisoner is innocent (accepting the null hypothesis) when actually he is guilty( the alternate hypothesis)

Thus, type II error would be setting free a guilty prisoner.

Option D) The prisoner is actually guilty and the jury sets him free.