A student claims that he can correctly identify whether a pe

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 he can correctly identify a business major 87% of the time, while 16% of the time he mistakenly identifies an agriculture major as a business major. Presented with one person and asked to identify the major of this person (who is either a business or 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.

1. Referring to Table above, what would be a Type I error?

a. Saying that the person is a business major when in fact the person is a business major.

b. Saying that the person is a business major when in fact the person is an agriculture major.

c. Saying that the person is an agriculture major when in fact the person is a business major.

d. Saying that the person is an agriculture major when in fact the person is an agriculture major.

2. Referring to Table above, what is the value of alpha?

a. 0.13

b. 0.16

c. 0.84

d. 0.87

3. Referring to Table above, what is the power of the test?

a. 0.13

b. 0.16

c. 0.84

d. 0.87

Solution

1. Type 1 error is the probability that the null hypothesis is rejected given it is true.

So, Answer:

c. Saying that the person is an agriculture major when in fact the person is a business major.

2. Alpha = type 1 error = P(saying agri major | business major) = 1 - P(saying business major | business major)

= 1 - 0.87 = 0.13 = 13%

Answer: a. 0.13

3. Power of test = P(saying agricultural major | agricultural major) = 1 - 0.16 = 0.84

Answer : c. 0.84

4. Beta = 1 - power = 1- 0.84 = 0.16

Answer: b. 0.16