When is a hypothesis test appropriate? For example, when would a hypothesis test bed used?
 A: That's a fair question and the answer relates to the difference between taking a population census and taking a sample. It depends of how the statistics of 3.1% and 4.5% were obtained. Do you have complete data or were the proportions estimated from a sample of your target population?
If you have complete data, i.e., if you know the total number of people who play basketball in your target population, then there is indeed no purpose in a hypothesis test. You already know the truth.
If the proportions were instead estimated by polling a random collection of people, say by telephone or by a questionaire, then a hypothesis test would be needed in order to confirm that the increase from 3.1% to 4.5% is statistically significant and likely to be representative of the whole population. The null hypothesis in this case would be that the proportion has not changed. As well as conducting a hypothesis test, it would also be useful to attach a "margin of error" to each of the proportions, as is often done for political polls.
