Suppose I have a bag of marbles containing 10 different colors. I know that white marbles are by far the most common color. My hypothesis is that black marbles are the second most common color in the bag. Eg. there are more black marbles in the bag than any other non-white color of marbles. I sample 1500 times with replacement and here is what I get.
- White: 1473
- Black: 10
- Blue: 1
- Green: 2
- Yellow: 4
- Brown: 1
- Purple 1
- Red: 2
- Orange: 1
- Pink: 3
- Grey: 1
- Indigo: 1
What test can I use to check whether the frequency for black is statistically significantly different from the other values? I heard Kruskal–Wallis should work, but I'm not sure.
Thanks
Take as a null hypothesis that the probability of any of the $27$ non-while balls being of any of the 11 possibilities is equal ($p_{hue}=1/11,\ hue=black, blue, \dots indigo$).
Now look at the probability of getting 11 or more of one colour in a sample of 27. That will allow you to test the hypothesis that there is no favoured $hue$ against that there is one. If you want the alternative to be that the favoured $hue$ is black you should be using the probability of getting 11 or more $black$ in the sample of 27.