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

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.

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.

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.

1 answer

To determine which statements are true regarding the described scatter plot of study hours and GPAs, let's analyze each statement:

  1. 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).
  2. 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.
  3. 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.
  4. 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.
  5. 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.