What is the expected correlation coefficient between hours awake and hours asleep over a 24-hour period?

The expected correlation coefficient between hours awake and hours asleep over a 24-hour period is -1.0. This value indicates a perfect negative linear relationship between the two variables.

As one variable increases (hours awake), the other variable (hours asleep) necessarily decreases. In a 24-hour cycle, the total hours awake and the total hours asleep must always add up to 24 hours. Therefore, if someone is awake for a longer period, they must be asleep for a shorter duration, creating a direct inverse relationship.

A correlation of -1.0 signifies that for every additional hour awake, there is a corresponding hour less of sleep. This scenario encapsulates the perfect negative correlation expected between these two measurements, effectively demonstrating that as one variable rises, the other declines in exact proportion.