Consider the test of $H_0$ : The defendant is not guilty against $H_a$ : The defendant is guilty.

a$.$ Explain in context the conclusion of the test if $H_0$ is rejected.

b$.$ Describe the consequence of a Type I error.

c$.$ Explain in context the conclusion of the test if you fail to reject $H_0.$

d$.$ Describe the consequence of a Type II error.

a$.$ Explain in context the conclusion of the test if $H_0$ is rejected.

A$.$ Rejecting $H_0$ implies that the null hypothesis, the defendant is not guilty, is false. The defendant is therefore, found guilty and sentenced$.$

B$.$ Rejecting $H_0$ implies that the null hypothesis, the defendant is not guilty, is true. The defendant is therefore, found not guilty and set free.

C$.$ Rejecting $H_0$ implies that the null hypothesis, the defendant is guilty, is false. The defendant is therefore, found not guilty and set free.

D$.$ Rejecting $H_0$ implies that the null hypothesis, the defendant is guilty, is true. The defendant is therefore, found guilty and sentenced$.$

b$.$ Describe the consequence of a Type I error.

A$.$ A type I error would result in an innocent defendant being set free and not being convicted.

B$.$ A type I error would result in a guilty defendant being acquitted for lack of evidence.

C$.$ A type I error would result in an innocent defendant being convicted for a crime they did not commit.

D$.$ A type I error would result in a guilty defendant being set free and not being convicted.