To evaluate the statements provided about the scatter plot showing the relationship between hours studied and GPA, we can analyze each statement based on general principles of statistics and relationships between variables.
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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 indicates that there is a tendency for higher study hours to correlate with higher GPAs, but it does not imply a guaranteed outcome. It's a probabilistic relationship.
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The slope of the line of best fit will be positive and the y-intercept will also be positive.
- Not necessarily True. While the slope may be positive (indicating a positive correlation), the y-intercept can be zero or negative depending on the data points in the scatter plot. The y-intercept being positive is not a guaranteed conclusion.
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Your GPA should be 0 when you study 0 hours each week.
- Not necessarily True. This statement assumes the y-intercept is at (0, 0), which is not always the case. It's possible for students to have a GPA without studying at all, depending on the data from the survey.
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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.
- Not necessarily True. A deterministic interpretation suggests a guaranteed outcome based on the input. While it may be likely that studying 20 hours correlates with a GPA of at least 3.0, it cannot be asserted as a certainty without additional analysis of the data.
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The relationship is a positive linear relationship.
- True. If the scatter plot shows a trend where higher values of x (study hours) correspond to higher values of y (GPA), then this indicates a positive linear relationship.
Based on this analysis:
- True statements: 1 and 5
- False statements: 2, 3, and 4
So, the true statements selected are 1 and 5.
1 answer