Question

if there is a positive correlation between the amount of sleep a student receives and reported levels of anger, this means that as the amount of sleep decreases, anger: decreases. increases. does not increase or decrease. is caused by a lack of sleep.

Explanation:

A positive correlation means that two variables change in the same direction. So if sleep (one variable) decreases, the other variable (anger) should also change in the same direction as the first variable's decrease? Wait, no—wait, positive correlation is when both increase or both decrease. Wait, let's clarify: positive correlation: as one increases, the other increases; as one decreases, the other decreases. So if sleep decreases, anger (with positive correlation) should also decrease? Wait, no, wait the options: wait the question is "as the amount of sleep decreases, anger:". Wait, positive correlation: sleep and anger are positively correlated, so when sleep increases, anger increases; when sleep decreases, anger decreases. Wait but the options: the first option is "decreases", second is "increases". Wait, maybe I got it wrong. Wait, no—wait, positive correlation: two variables move together. So if sleep goes down, anger goes down. But let's check the options. Wait, maybe I made a mistake. Wait, let's re-express: positive correlation: \( \text{sleep} \) and \( \text{anger} \) have a positive relationship, so \( \text{sleep} \uparrow \implies \text{anger} \uparrow \), and \( \text{sleep} \downarrow \implies \text{anger} \downarrow \). So when sleep decreases, anger decreases. But wait, the first option is "decreases". But wait, maybe I messed up. Wait, no—wait, the question is about positive correlation. So the correct answer should be that as sleep decreases, anger decreases. But let's check the options again. Wait, the options are:

• decreases.

• increases.

• does not increase or decrease.

• is caused by a lack of sleep.

Wait, but positive correlation is about direction of change, not causation. So the last option is wrong (correlation doesn't imply causation). The third option is wrong (they do change). Now, positive correlation: same direction. So if sleep decreases, anger decreases. So the first option? Wait, but maybe I got it reversed. Wait, no—let's think of an example: if height and weight are positively correlated, as height increases, weight increases; as height decreases, weight decreases. So same with sleep and anger: positive correlation, so when sleep (x) decreases, anger (y) decreases. So the answer should be "decreases"? Wait, but the second option is "increases". Wait, maybe I made a mistake. Wait, no—wait, positive correlation: the two variables move in the same direction. So if x (sleep) decreases, y (anger) decreases. So the first option is correct? Wait, but let's check again. Wait, the question says "positive correlation between the amount of sleep a student receives and reported levels of anger". So sleep (x) and anger (y) have \( r > 0 \). So when x decreases, y decreases. So the answer is "decreases" (first option). Wait, but maybe the options are labeled differently. Wait, the first option is "decreases", second is "increases". Wait, maybe I got it wrong. Wait, no—positive correlation: same direction. So if sleep goes down, anger goes down. So the first option is correct.

Answer:

A. decreases.