In: Statistics and Probability
A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time. When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or an agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major. What would be a Type II error?
Saying that the person is an agriculture major when in fact the person is an agriculture major.
Saying that the person is a business major when in fact the person is a business major.
Saying that the person is a business major when in fact the person is an agriculture major.
Saying that the person is an agriculture major when in fact the person is a business major.
Answer:
Given that,
A student claims that he can correctly identify whether a person is a business major or an agriculture major, by the way, the person dresses.
Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time.
When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time.
Presented with one person and asked to identify the major of this person (who is either a business or an agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.
What would be a Type II error:
For Type II error,
Option C (3rd ) is correct.
3. Saying that the person is a business major when in fact the person is an agriculture major.
Explanation:
Type II error: Accept H0 when it is false.
i.e,
The type II error is to accept the null hypothesis when it is false.
The null hypothesis:
H0: the person is a business major and the alternative hypothesis,
H1: the person is an agriculture major.
Thus the type II error is Saying that the person is a business major when in fact the person is an agriculture major.