56. A psychology professor wants to examine the relation between amount of sleep and test performance. The professor asks the students to write down how long they had slept the night before the final exam. The results showed a correlation of -.70 between the amount of sleep students reported and their exam scores. Which of the following best describes the results of the study?
Answer: C
The less students slept, the higher their exam scores were.
The correlation of -.70 indicates a strong negative relationship between the amount of sleep and exam scores, suggesting that as the amount of sleep decreases, exam scores tend to increase.
A) There was no relation between the amount of sleep and the exam scores.
This option is incorrect because the correlation of -.70 clearly demonstrates a significant relationship between the variables, indicating that there is indeed a relation.
B) The professor made an error in the calculations because correlations can only be positive.
This option is also incorrect. Correlations can be both positive and negative; a negative correlation simply indicates an inverse relationship between the variables, which is valid in this context.
C) The less students slept, the higher their exam scores were.
This statement accurately reflects the findings of the study. The negative correlation signifies that lower amounts of sleep are associated with higher exam scores, which aligns perfectly with the correlation provided.
D) The amount of sleep accounted for 70% of the variance of students' exam scores.
This option is misleading. While the correlation coefficient of -.70 does indicate a strong relationship, it does not directly imply that 70% of the variance is accounted for in the way regression analysis might. Correlation does not equate to variance explanation in this manner.
Conclusion
The correct answer, "The less students slept, the higher their exam scores were," is supported by the strong negative correlation identified in the study. All other options misinterpret the nature of correlation or the results, failing to accurately represent the relationship between sleep and test performance as indicated by the data.