Question

In the Country A legal​ system, a defendant is presumed innocent until proven guilty. Consider a null​ hypothesis, Upper H 0​, that the defendant is​ innocent, and an alternative​ hypothesis, Upper H 1​, that the defendant is guilty. A jury has two possible​ decisions: Convict the defendant​ (i.e., reject the null​ hypothesis) or do not convict the defendant​ (i.e., do not reject the null​ hypothesis). Explain the meaning of the risks of committing either a Type I or Type II error in this example.

Answer 1

Answer:

Type 1 error: If the defendant is innocent and jury convict the defendant

Type 2 error : If the defendant is guilty and jury do not convict the defendant.

Explanation:

Given : Null hypothesis : $H_0:$ the defendant is​ innocent .

Alternative hypothesis : $H_1:$ the defendant is guilty.

A jury has two possible​ decisions: Convict the defendant​ (i.e., reject the null​ hypothesis) or do not convict the defendant​ (i.e., do not reject the null​ hypothesis).

We know that Type 1 error is a false positive statement that you reject the true null hypothesis.

i.e. If the defendant is innocent and jury convict the defendant then it is the Type 1 error.

Type 2 error is a false negative statement that you do not reject the false null hypothesis.

i.e. If the defendant is guilty and jury do not convict the defendant then  it is the Type 2 error.