34. 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 results of the study indicate a strong negative correlation of -.70, suggesting that as the amount of sleep decreases, exam scores tend to increase. This counterintuitive finding implies that students who reported less sleep performed better on the exam.
A) There was no relation between the amount of sleep and the exam scores.
This option is incorrect because a correlation of -.70 indicates a significant relationship between the amount of sleep and exam scores. A correlation of zero would suggest no relationship, which is not the case here.
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 correlation of -.70 is valid and indicates a strong inverse relationship, meaning that the professor did not make an error in the calculations.
C) The less students slept, the higher their exam scores were.
This option accurately reflects the findings of the study. The negative correlation indicates that lower amounts of sleep corresponded with higher exam scores, which is a key insight derived from the reported data.
D) The amount of sleep accounted for 70% of the variance of students' exam scores.
This option is misleading. While the correlation coefficient is -.70, this does not mean that sleep accounts for 70% of the variance. To find the proportion of variance explained, one would square the correlation coefficient, resulting in approximately 49%, not 70%.
Conclusion
The correct answer, C, highlights the surprising relationship where less sleep is associated with higher exam scores, as indicated by the strong negative correlation of -.70. Options A and B misunderstand the nature of correlation, while option D misinterprets the variance explained by the correlation. Therefore, C is the only option that accurately describes the findings of the study.