Suppose the company's claim was different that the one above. Suppose they claimed that 20% of their mixed nuts are cashews, 30% are almonds, and the rest are peanuts and that a machine counts out exactly 20% cashews, 30% almonds, and 50% peanuts into each bag of 200. To test their claim I bought a package of their mixed nuts. It contained 200 nuts. I counted 28 cashews, 50 almonds, and 122 peanuts
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.
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.
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
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.
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
Which one is correct?