Question

Suppose that Ricardo and Anita attend different colleges. Ricardo’s GPA is the same as the average GPA at his school. Anita’s GPA is 0.70 standard deviations above her school average. In complete sentences, explain why each of the following statements may be false.

a) Anita's GPA is higher than Ricardo's GPA.
b) Anita's GPA is exactly 0.70 points higher than Ricardo's GPA.
c) Anita's GPA is at least 0.70 points higher than Ricardo's GPA.
d) Ricardo's GPA is lower than the school average.

Answer 1

An explanation of why each statement may be false, regarding the comparison between Ricardo and Anita's GPAs and their school averages.

Step-by-step explanation:

In order to explain why each of the statements may be false, we need to understand the relationship between GPA and standard deviations. GPA is a measure of a student's academic performance, while standard deviation represents the spread of data around the average.

a) Statement a may be false because Anita's GPA is 0.70 standard deviations above her school average, which means her GPA could be lower than Ricardo's GPA, especially if Ricardo's GPA is close to the school average.

b) Statement b may be false because Anita's GPA being 0.70 standard deviations above Ricardo's does not necessarily mean it is exactly 0.70 points higher.

The exact difference would depend on the actual GPAs and the standard deviation.

c) Statement c may be false because Anita's GPA being 0.70 standard deviations above Ricardo's does not guarantee that the difference is at least 0.70 points.

The actual difference would depend on the actual GPAs and the standard deviation.

d) Statement d may be false because Ricardo's GPA being the same as the average GPA at his school does not imply it is lower. It could be equal to or higher than the school average.