Instruction 9-1
A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses. Suppose in actuality that if someone is studying a business major, she can correctly identify that person as a business student 87% of the time. When a person is studying a science major, the student will incorrectly identify that person as a business student 16% of the time. Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major), she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student.
-Referring to Instruction 9-1,what is the "actual level of significance" of the test?
A) 0.13
B) 0.16
C) 0.84
D) 0.87

Question

Quizplus · Accepted Answer

The actual level of significance is the probability of Type I error, which is the probability of rejecting the null hypothesis when it is actually true. In this case, the null hypothesis is that the person is a business student. If the student identifies the person as a business student, it means she accepts the null hypothesis. If she identifies the person as a science student, she rejects the null hypothesis.

The probability of rejecting the null hypothesis when it is actually true is the probability of identifying a science student as a business student, which is 16%. Therefore, the actual level of significance (or the probability of Type I error) is 0.16. However, the question asks for the probability of correctly identifying a business student, which is 87%. Therefore, the probability of correctly accepting the null hypothesis (or correctly identifying a business student) is 1 - 0.16 = 0.84.

Since the question asks for the actual level of significance, the answer is A) 0.13, which is the probability of rejecting the null hypothesis when it is actually true.

Instruction 9-1 a Student Claims That She Can Correctly Identify Whether a Whether