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)
Responses
We 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.
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.
Your GPA should be 0 when you study 0 hours each week.
The statement "Your GPA should be 0 when you study 0 hours each week" is FALSE.
The statements that are TRUE based on the scatter plot are:
1. It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
2. The slope of the line of best fit will be positive and the y-intercept will also be positive.
3. The relationship is a positive linear relationship.
The statement "Your GPA should be 0 when you study 0 hours each week" is not supported by the scatter plot, as there are data points with non-zero GPAs for students who study 0 hours per week.
To determine which statements are true, let's analyze the given information and the scatter plot.
First, let's understand the terms "deterministic interpretation" and "probabilistic interpretation".
- Deterministic interpretation: In this context, it means that there is a direct causation or predictable relationship between the number of hours studying and the resulting GPA. If we use a deterministic interpretation, we can confidently make predictions about individual students based on their study hours.
- Probabilistic interpretation: It means that there is a correlation or relationship between study hours and GPA, but it is not necessarily a direct causation. The relationship might not be the same for every student, and there could be other factors at play. If we use a probabilistic interpretation, we can reasonably expect that more study hours are associated with higher GPAs, but it is not a guarantee for every individual student.
Now, let's examine the statements:
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 not necessarily true because the scatter plot does not provide a perfect line of best fit. Some students who studied 20 hours have GPAs below 3.0. Therefore, we cannot confidently predict that every student who studies 20 hours will achieve a 3.0 GPA.
2. It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
This statement is true. As we observe the scatter plot, there is a general trend that students who study more hours tend to have higher GPAs. However, there is still some variation, indicating that the relationship might not be the same for each student.
3. The slope of the line of best fit will be positive, and the y-intercept will also be positive.
Looking at the scatter plot, it appears that there is a positive slope and a positive y-intercept. This means that as the number of hours studied increases, the expected GPA also increases. So, this statement is true.
4. The relationship is a positive linear relationship.
From the scatter plot, we can observe a positive trend, meaning that as study hours increase, the GPAs also tend to increase. This indicates a positive relationship. Therefore, this statement is true.
5. Your GPA should be 0 when you study 0 hours each week.
Based on the scatter plot, there are some students who have a GPA of 0 even when they studied for 0 hours per week. Therefore, it is possible for the GPA to be 0 when study hours are 0. Thus, this statement is true.
In summary, the following statements are true:
- 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 be positive, and the y-intercept will also be positive.
- The relationship is a positive linear relationship.
- Your GPA should be 0 when you study 0 hours each week.