Question

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). Looking at the graph, which statements are TRUE?(3 points)ResponsesWe can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.We can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.Your GPA should be 0 when you study 0 hours each week.Your GPA should be 0 when you study 0 hours each week.The slope of the line of best fit will be positive and the y-intercept will also be positive.The slope of the line of best fit will be positive and the y-intercept will also be positive.The relationship is a positive linear relationship.The relationship is a positive linear relationship.Skip to navigation

Answer 1

Based on the statements provided about the scatter plot showing the relationship between hours studied and GPAs, here are the analyses of each statement:

1. We can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.

   • This statement is FALSE. In a deterministic interpretation, we would assert a specific outcome. However, without knowing the exact distribution of the data, we cannot claim that a particular GPA is guaranteed at a given number of study hours.

2. It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.

   • This statement is TRUE. This reflects a probabilistic relationship where increased study hours are associated with higher GPAs, but it does not imply a guaranteed outcome.

3. Your GPA should be 0 when you study 0 hours each week.

   • This statement is NOT necessarily TRUE. While it could be true depending on the specific data of the students surveyed, it is not a definitive statement without further evidence from the scatter plot indicating that this is the case.

4. The slope of the line of best fit will be positive and the y-intercept will also be positive.

   • This statement may be TRUE, depending on the data distribution shown in the scatter plot. A positive slope would indicate a positive correlation, while a positive y-intercept would mean that when study hours are zero, the GPA is above zero.

5. The relationship is a positive linear relationship.

   • This statement is TRUE, assuming the scatter plot shows that as the number of hours studied increases, the GPAs also increase.

In summary, the TRUE statements based on typical interpretations of such scatter plot data would likely be:

• It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
• The slope of the line of best fit will likely be positive (though the positivity of the y-intercept is not guaranteed without additional information).
• The relationship is a positive linear relationship, assuming the data exhibits a trend in that direction.

Therefore, the statements you can confidently mark as true are typically points 2 and 5.