Question

a scatterplot is produced to compare the number of hours that students study to their test scores. there are 25 data points, each representing a different student. the scatterplot shows a grouping of points rising from left to right. which statement could be true?

• there is no relationship between the number of hours that students study and their test scores because the scatterplot does not have a cluster.
• as the number of hours of studying increases, test scores decrease because the scatterplot has a cluster that increases from left to right.
• as the number of hours of studying increases, test scores increase because the scatterplot has a cluster that increases from left to right.
• the number of hours that students study is equal to the test scores because the scatterplot does not show a cluster.

Explanation:

1. Analyze the first option: The scatterplot has a grouping (cluster) of points rising from left to right, so there is a relationship, and it does have a cluster. Eliminate this option.
2. Analyze the second option: A cluster rising from left to right indicates a positive relationship (as one variable increases, the other increases), not a decrease. Eliminate this option.
3. Analyze the third option: A cluster of points rising from left to right in a scatterplot represents a positive correlation, meaning as study hours (x - variable, left - to - right on the x - axis) increase, test scores (y - variable) increase. This matches the description.
4. Analyze the fourth option: The scatterplot does show a cluster, and study hours and test scores are not necessarily equal (correlation is not causation of equality). Eliminate this option.

Answer:

C. As the number of hours of studying increases, test scores increase because the scatterplot has a cluster that increases from left to right.