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The compelling evidence used in critical thinking and the court of law is proof. A proof is an evidence that verifies all the conclusions and facts that were stated by a party. It supports to establish the truth of a statement. It is also a strong type of evidence that is directly confirming the truth.
Bibliographic review - Search for trustworthy sources about how listening to music affects studying and in the case there are none about this topic specifically, find enough information about music, studying and their interactions for you to develop enough knowledge to develop the experiment.
Introduction - Have a well established reason on why it is important to understand this situation, why it helps or not and how could this information benefit you or the reader.
Methods - Develop a routine for this experiment which would show the differences between listening to music or not. This could be studying for a couple tests without listening to music and then studying for a same number of tests whilst doing so. It is important to not depend on a single test, once it could not represent the truth. The higher the number of experiments, the better.
Results and conclusion - Having in mind all the bibliographic review you did and the results you got from the tests, compare the grades and the highest medium should be the best options, allowing you to conclude whether listening to music affects or not the studying and if the affects it has are positive or negative.