If we can't translate the situation into a null box is there still a way to test their claim? For example, let's say the company claims that the nuts are carefully counted to ensure that every single package has exactly 20% cashews, 30% almonds, and 50% peanuts, can we still test their claim?

a. Yes, we can still do a chi square test but we would have to adjust the numbers above since the expected values would have no error at all.
b. Yes, because the company is still making a claim about the distribution of the nuts it puts into the packages, we can test that claim the same way we did above.
c. No, there is no way to test a claim with a significance test when a situation cannot be translated into a box model. So there is no way to test their claim, period.
d. Yes, however, we cannot use a significance test. We can still test the claim by common sense, just by buying a few packages and seeing that they're not doing what they say.
e. Yes, we can still do a chi square test because the situation is essentially identical to the one above. A box model never enters into our calculations so we can proceed with the same test and the same conclusions.