Question

a health organization collects data on hospitals in a large metropolitan area. the scatterplot shows the relationship between two variables the organization collected: the number of beds each hospital has available and the average number of days a patient stays in the hospital (mean length of stay).
hospitals
which statement best explains the relationship between the variables shown?
hospitals with more beds cause longer lengths of stay.
the size of the hospital does not appear the have an influence on length of stay.
more complex medical cases are often taken by larger hospitals, which increases the lengths of stay for larger hospitals.
more complex medical cases are often taken by larger hospitals, which decreases the lengths of stay for larger hospitals.

Explanation:

Step1: Analyze scatterplot trend

The scatterplot shows that as the number of beds (hospital size) increases, the mean length of stay generally increases. This indicates a positive relationship.

Step2: Evaluate each option

• Option1: Incorrect, as correlation ≠ causation.
• Option2: Incorrect, since there is a visible positive trend.
• Option3: Correct, it explains the positive trend by linking larger hospitals to complex cases (which require longer stays).
• Option4: Incorrect, complex cases would increase (not decrease) stay length.

Answer:

C. More complex medical cases are often taken by larger hospitals, which increases the lengths of stay for larger hospitals.