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I have data that shows the number of disease cases in the summer versus the winter for 40 different sites. For example: 

        Winter   Summer
site 1   133       23
site 2   198       11
site 3   2029      131
...      ...       ...

There are substantial differences in the ratio of summer-to-winter cases across sites and I want to know for which sites this summer-to-winter ratio is significantly different than expected. Specifically, I want a test that tells me which sites have a significantly different (larger or smaller) than expected based on all the data. I should also note that the number of cases varies significantly across sites.

I have done similar tests in the past using a bootstrap/percentile method, but I was wondering if there was a standard method for this situation. Thanks for any help in advance!

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