Apologies if this is a really dumb question, at the moment I'm at a loss. I need help figuring out which statistical test to use for a case that's similar to the following scenario:
Say my hypothesis is that the distribution of favorite color is different on the West Coast versus East Coast.
I went out to the West Coast and took a sample of 1000 people and surveyed what their favorite color is. There are 30 possible colors to choose from, and for each color, I tabulated the number of people that reported it's their favorite. Then I sampled another 1000 unrelated people (assuming independent sampling) doing the same. Then I repeated this process say 8 more times. Now I have a mean number of people that prefers each of the 30 colors, as well as the SE.
Next, I went to the East Coast and repeated the procedures in the above paragraph.
Now, I have two distributions that measure the same thing (color preferences), and the variable has 30 categories (individual color). I know the mean and SE for each categories within these two distributions. What test should I use to see if the color preference distribution is different between East Coast and West Coast? I feel like I'm just getting confused by the 30 categories thing and overthinking it.