In reply to Mike Dansberry.

At that sample size all colors appear significantly different from either factory distribution with only brown having a 1.3% chance of getting 364 (or fewer) brown out of 3248 samples when one would expect 406 browns given the nominal proportion from the Hackensack being 12.5% brown

The question I have is how to best utilize all 6 ratios in a single, more sensitive, hypothesis test calculating the probability of all 6 deviations from the nominal proportions. In other words, how would one calculate the overall probability of the sample coming from a specific factory given the test data?

Question #2: How would I determine the probability that the sample contains a "mix" from both factories? In both this sample and the Brazilian sample in the earlier comments the samples do not appear to be a mix of the two factories