Sometimes we cannot design and perform our own experiment to test an idea and need to use an experiment that was already performed by somebody else. Why is it still important to make a prediction based on the idea being tested before we look at the data from that experiment?

Because sometimes the predictions we make are as same as the data used in someone's other other experiment that you're going to read. Making observations and prediction data about an experiment may be very satisfactory for you when you came to know that you have independently predicted the correct values or conditions used in a perfect experiment. That is all related to your IQ.