Suppose I have a number of widgets that are independently produced in a number of different categories (for example, 5 different categories). Each of these categories has a listed probability of the widget getting produced in that category. For example, group A has a 0.1 probability, P(B) = 0.2, P(C) = 0.15, etc, so they add up to 1.
If I was to randomly select a bunch of these widgets and count the number of widgets in each category, how would I run a hypothesis test to accept or reject the probabilities as a whole that have been given based on my sample? Do I need to run multiple tests?
I don't even know where to start on this one, so any tips would be greatly appreciated! Thanks!