If a teacher wants to test her belief that more than five students in college classes typically receive A as a grade, she'll perform _______-tail testing of a mean.


A. right
B. one
C. left
D. two

The correct answer is D. two-tail testing.

To understand why two-tail testing is the correct choice, let's first break down the question.

The teacher wants to test her belief that more than five students in college classes typically receive A as a grade. This implies that she is interested in determining if the mean number of students receiving A grades is significantly different from five, but she does not have a specific direction in mind (i.e., she just wants to see if it is different, whether it is more or less).

In hypothesis testing, the directionality of the alternative hypothesis determines the type of test to use. The alternative hypothesis is the one that states the claim or belief we are testing. In this case, the alternative hypothesis can be written as:

H1: The mean number of students receiving A grades is not equal to five.

Since this alternative hypothesis does not have a specific direction (i.e., it does not state that the mean is specifically greater or smaller than five), we need to use a two-tail test. A two-tail test splits the rejection region into two equal parts, allowing for the possibility of a significant difference in either direction (greater or smaller than the hypothesized value).

On the other hand, if the teacher's belief was specifically that more than five students typically receive A grades (i.e., she had a one-sided expectation), then we would use a one-tail test. In that case, the answer would be A. right because we would be specifically interested in the right tail of the distribution, testing whether the mean is significantly greater than five.

But since the teacher is interested in testing if there is a significant difference, regardless of direction, we use a two-tail test. Therefore, the correct answer is D. two.