What is a possible hypothesis for a situation where the manipulated variable is the number of recycling posters and the responding variable is the amount of aluminum cans in the courtyard.
Your original posting did not include an actual question. I have edited in a way that reflected what I thought you were trying to ask. I hope I have made the correct assumption about what you wanted to know.
I assume in this scenario that we are thinking about a courtyard where there are posters encouraging people to recycle. We are looking at how many of the posters are up and we are looking at the number of aluminum cans that are simply thrown on the ground in the courtyard. We are trying to create a hypothesis about the relationship between the number of posters and the amount of trash.
In any experiment (whether it is in the “hard” sciences or the social sciences), researchers are trying to find out how a change in one variable affects another variable. In experiments, researchers generally try to alter one of the variables intentionally. This variable is called the manipulated variable. (It can also be called the independent variable.) When they alter the value of the manipulated variable, they look to see if there is a change to the responding variable (which can also be called the dependent variable). Before they set up the experiment, they generally have a hypothesis which sets out how they think the responding variable will change when the researchers change the manipulated variable.
So, we need to have a hypothesis predicting how the amount of improperly discarded aluminum cans will change when the number of posters is changed by the researchers. There are at least two possible hypotheses. The first hypothesis is that a greater number of posters will lead to a lower amount of trash. Some teachers like to see hypotheses stated in an “if, then, because” format. If you need to put your hypothesis in this format, it could be “If the number of posters increases, the amount of trash will decrease because people will be more likely to see the posters and be persuaded to recycle.” The second hypothesis is that a larger number of posters will actually lead to more trash. This could be stated as “If the number of posters increases, the amount of trash will also increase because people will rebel against being told what to do by the posters.”
Either of these hypotheses is potentially correct. You will need to decide which one you think is more plausible and use it as the answer to your question.