To determine which graph best models the relationship between hours studied and student performance on a 15-question test, we would want to look for a graph that likely shows a positive correlation—meaning that as hours studied increases, student performance also tends to increase. Additionally, we would want to see clear data points that reflect this relationship.
Here’s a brief analysis of each option:
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Option A: It mentions "twenty-three points are plotted," but there is no description indicating if the relationship is positive, negative, or scattered.
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Option B: This option is identical to Option A, so the same analysis applies.
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Option C: This contains sixteen data points and specifies that they are plotted on a scatterplot. Scatterplots are generally well-suited for showing relationships between two continuous variables, like hours studied and test scores.
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Option D: This mentions "thirty points are plotted," but it has ranges of both axes from 0 to 16, which could indicate a much different relationship. It’s also unclear how performance is measured based on this range.
Considering the information above, Option C is likely the best choice because scatterplots are specifically designed to represent the relationship between two variables, which is exactly what you need to model the relationship between hours studied and student performance.