Question

Identify the type I error and the type II error that corresponds to the given hypothesis.

The proportion of settled medical malpractice suits is 0.23. Which of the following is a type I error?

A. Fail to reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually different from 0.23.

B. Reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually 0.23.

C. Reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually different from 0.23.

D. Fail to reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually 0.23.

Which of the following is a type II error?

A. Reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually 0.23.

B. Reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually different from 0.23.

C. Fail to reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually 0.23.

D. Fail to reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually different from 0.23.

Answer 1

Type I error : Option B

Type II error : Option D

Explanation:

We are given that the proportion of settled medical malpractice suits is 0.23,i.e.;

Null Hypothesis,
`H_0` : p = 0.23 {means proportion of settled malpractice suits is actually 0.23}

Alternate Hypothesis,
`H_1` : p
`\\eq` 0.23 {means proportion of settled malpractice suits is actually different 0.23}

Now, Type I error states the Probability of rejecting null hypothesis given the fact that null hypothesis was true.

So, in our question Type I error is Rejecting the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually 0.23.

Also, Type II error states the Probability of accepting null hypothesis given the fact that null hypothesis was false.

So, in our question Type II error is Fail to reject the claim that the proportion of settled malpractice suits is 0.23 when the proportion is actually different from 0.23.

Answer 2

The type I error is option B

The type II error is option D

Explanation:

The claim is that the proportion of settled medical malpractice suits is 0.23 which is the null hypothesis

Making a type I error means that the null hypothesis is rejected when it is actually true

Making a type II error means that the null hypothesis is accepted when it is false