To determine which statements are TRUE based on the description of the scatter plot, we can analyze each statement:
A. It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
- TRUE. This statement reflects a correlation rather than a definitive cause-and-effect relationship. While there may be a trend indicating that increased study hours are associated with higher GPAs, this does not guarantee it for every individual.
B. We can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.
- FALSE. A deterministic interpretation would imply a direct cause-and-effect relationship where one can predict the outcome consistently. However, individual performances can vary widely, and it's not guaranteed that a student studying 20 hours will achieve a specific GPA.
C. Your GPA should be 0 when you study 0 hours each week.
- FALSE. While it might be reasonable to assume that not studying at all could lead to low performance, it isn’t accurate to state that their GPA must be exactly 0. GPAs can vary and depend on various factors.
D. The relationship is a positive linear relationship.
- TRUE. If the scatter plot displays a trend where increased study hours correspond to increased GPAs, this would indicate a positive linear relationship.
E. The slope of the line of best fit will be positive and the y-intercept will also be positive.
- TRUE (assuming the relationship mentioned in D holds true). If the line of best fit has a positive slope, then it suggests that as study hours increase, GPAs increase too. A positive y-intercept would mean that GPA begins above 0 when study hours are at 0.
Based on the analysis above, the TRUE statements are:
- A
- D
- E
So, the correct selections are: A, D, and E.