A student claims that he can correctly identify whether a person is a business major or...

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.

Solutions

Expert Solution

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.

orchestra answered 11 months ago

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