Identify the direction and all possible interpretations of each of the following correlations. Be sure to identify each example as positive, negative, or zero (not correlated). Then give all possible causal interpretations for the results.

Many students in Professor Handel’s class express that they want a review session. Professor Handel agrees to hold an open review session for two hours the day before the exam. He then has his TA write down when each student arrives at the session and when they depart. When the exams are graded, Professor Handel announces there will be no more review sessions. The longer students spent at the review session the lower their score on the exam.

For positive correlation both variables increase/decrease together.

For negative correlation, one variable increases, while the other decreases.

If there is a correlation significantly greater than chance, either one variable causes the other or a third variable might be effecting the other two.

I'll let you do the interpretations.

negative correlation

interpretation that the longer the students reviewed impacted their exam grade

To identify the direction and possible interpretations of the correlations in this scenario, we need to look at the relationship between the duration of the review session attended by the students and their scores on the exam.

Based on the information provided, it is mentioned that the longer students spent at the review session, the lower their score on the exam. This implies a negative correlation between the duration of the review session and the exam scores.

Negative correlation: The longer students spent at the review session, the lower their exam scores.

Causal interpretations:

1. Distraction and focus: One possible causal interpretation could be that the longer students spent at the review session, the more they got distracted or lost focus. Instead of utilizing the time effectively, they may have been engaged in less productive activities or failed to concentrate on the relevant material.

2. Lack of preparation: Another possible interpretation could be that students who needed more review time were less prepared for the exam. Spending a longer duration at the review session could indicate a lack of understanding or retention of the course material.

3. Overconfidence: It is also possible that some students who spent a longer time at the review session were overconfident in their knowledge and underestimated the difficulty of the exam. As a result, they might have had a false sense of security during the review session, leading to less effort or focus on the important concepts.

4. Study strategies: The duration of the review session could also reflect variations in study strategies. Students who spent a shorter time might have employed more effective study techniques, allowing them to comprehend the material more efficiently, while those who spent a longer duration might have used less effective strategies or were inefficient in their studying.

Remember, these interpretations are hypothetical and based on the given scenario. Additional information and more extensive analysis would be required to draw concrete conclusions.