Final answer:
The correct statement is that both the size of the bucket and the popcorn's freshness were independent variables, manipulated to observe their effect on a dependent variable, the amount of popcorn eaten. This means that both the size of the bucket and the popcorn's freshness were manipulated by the researchers to observe the effect on the amount of popcorn eaten by moviegoers, which is the dependent variable.
Step-by-step explanation:
In the study described, where moviegoers were given either medium or large buckets of popcorn filled with either fresh or stale popcorn, the correct statement is that the size of the bucket was an independent variable and the popcorn's freshness was also an independent variable. This means that both the size of the bucket and the popcorn's freshness were manipulated by the researchers to observe the effect on the amount of popcorn eaten by moviegoers, which is the dependent variable.