TABLE 9-2
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.
-Referring to Table 9-2, what is the power of the test?
A) 0.13
B) 0.16
C) 0.84
D) 0.87

Question

Quizplus · Accepted Answer

Power of the test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. Here, the alternative hypothesis is that the person is an agriculture major. The power of the test can be calculated using the formula:

Power = P(reject null hypothesis | alternative hypothesis is true)

= P(correctly identify as agriculture major | person is agriculture major)

= 1 - P(incorrectly identify as business major | person is agriculture major)

= 1 - 0.16

= 0.84

Therefore, the best choice is C, which corresponds to a power of 0.84.

TABLE 9-2 a Student Claims That He Can Correctly Identify Whether a Whether