The scatter plot shows the data collected from a survey of 19 students, in which they were asked how many hours per week they study (x) and what their GPAs are (y).

Question

Looking at the graph, which statements are TRUE?

A. It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
B. We can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.
C. Your GPA should be 0 when you study 0 hours each week.
D. The relationship is a positive linear relationship.
E. The slope of the line of best fit will be positive and the y-intercept will also be positive.

Answer 1

To evaluate the statements regarding the scatter plot based on the relationship between hours studied (x) and GPA (y), we need to breakdown each statement:

A. True. It is correct to interpret that there is a probabilistic relationship where more study hours may lead to a higher GPA, but it is not guaranteed for every individual student.

B. False. A deterministic interpretation implies certainty, which is unlikely since we cannot definitively say that a student who studies for 20 hours will achieve at least a 3.0 GPA without more data.

C. False. While it might be expected that studying less would likely lead to lower GPAs, a GPA of 0 when studying 0 hours is not a stringent rule; other factors could affect a student's GPA.

D. True. If the scatter plot shows that as study hours increase, GPAs tend to also increase, this indicates a positive linear relationship.

E. False. Although the slope of the line of best fit might be positive if there is a positive relationship, the y-intercept being positive depends on how the data is distributed. If the line of best fit extends below the origin, the y-intercept could easily be negative.

In summary, the true statements based on typical interpretations of scatter plots in this context are A and D.