Question

1. a study of 100 randomly selected students from first through sixth grade finds a strong correlation between height and reading ability. can you conclude that being taller causes students to read better? why or why not?

1. a strong positive correlation between two variables a always b sometimes c never indicates causation.

Explanation:

Question 17 (Analysis of Correlation and Causation)

To determine if height causes better reading ability, we analyze correlation vs. causation. Correlation (here, between height and reading ability) shows a relationship but doesn’t prove causation. In this study, students are from first - sixth grade. As grade (and age) increases, both height (students grow with age) and reading ability (improves with education/age) tend to increase. So, the correlation is likely due to a confounding variable (age/grade), not a direct causal link from height to reading ability. We can’t conclude height causes better reading because correlation doesn’t imply causation, and there’s a confounding variable (age/grade) influencing both.

A strong positive correlation between two variables sometimes indicates causation. For example, in the case of studying hours and exam scores, a strong positive correlation might be due to the causal relationship that more studying (variable 1) causes higher exam scores (variable 2). But in other cases, like the height - reading ability example, a strong correlation is due to a confounding variable (not causation). So a strong positive correlation sometimes indicates causation.

Answer:

No, we cannot conclude that being taller causes students to read better. Correlation does not imply causation. In this case, the students are from first through sixth grade, so as grade (and age) increases, both height (students grow with age) and reading ability (students' reading ability improves with education and age) tend to increase. So the correlation between height and reading ability is likely due to the confounding variable of age (or grade level), not a direct causal relationship from height to reading ability.

Question 18 (Correlation and Causation)