To determine which statements are true regarding the described scatter plot of study hours and GPAs, let's analyze each statement:
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It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
- True: This statement reflects the idea that while there may be a tendency for GPAs to increase with additional study hours, this is not guaranteed for every individual (hence it is probabilistic).
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Your GPA should be 0 when you study 0 hours each week.
- False: While one might expect that not studying at all could lead to a low GPA, it doesn't necessarily mean the GPA will be exactly 0. Other factors may influence GPA, and some students might still perform adequately.
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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 implies a strict cause-and-effect relationship, which is unlikely to be valid based on scatter plot data. Just because a student studies a certain number of hours does not guarantee a specific GPA.
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The slope of the line of best fit will be positive and the y-intercept will also be positive.
- False (likely): While the slope could be positive (indicating a general trend where GPA increases with study hours), the y-intercept being positive depends on whether the plot includes data points for low study hours. It's possible the intercept could be zero or negative.
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The relationship is a positive linear relationship.
- True: If the scatter plot shows that as study hours increase, GPAs also tend to increase, then this supports the conclusion of a positive linear relationship.
In summary, the true statements are:
- It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
- The relationship is a positive linear relationship.