Statistical significance of birth month of professional boxers I looked at the birth dates of the top 100 ranked professional boxers of all time (67 of them to be exact).  40% of them were born during certain 3 month-long time periods.  If birth date of boxers were totally random (as we'd expect) than in any 3 month period, about 25% of boxers should be born during any 3 month period, but I found a period where it was 40%.  I found another 3 month period where only 12% of boxers were born.  Question is--is that 40% statistically significant compared to the expected 25%?  Same question for the 12% (is that statistically significant different from 25%)
I can't seem to figure out how to run the numbers.  As mentioned n = 67.
(Actually, birth month is not perfectly distributed--somewhat more people are born in summer months than winter but I think this should not affect the total 'story' here).  I very much appreciate any help.
 A: A basic approach
You should be able to find data on births by time of year for the population as a whole.
To see if there is evidence that boxers have a different distribution of birth dates, given your sample size I suggest you work at a granularity of "months". Your null hypothesis is that boxers' birth months follow the same distribution as the wider population. 
For each month you can calculate the "expected frequency" of boxer birthdays by multiplying your sample size by the proportion of people in the wider population who were born in that month.
You can then compare that to the "observed frequency" - the number of boxers who actually did have a birthday in that month. To determine if there is significant evidence of a difference between them, you can use a chi-squared goodness of fit test.
Issues with the basic approach
For a student working at an introductory level I'm hoping the above is an appropriately pitched answer. I don't think it is the "best" way to do things - for instance it throws away data on actual date of birth because it only looks at month, and it groups 1 Feb with 28 Feb despite it being close to Jan 31. Statisticians generally hate throwing away information from their data. This is really just a special case of binning or discretizing continuous data and that's well-known to be a bad idea.
More sophisticated approaches are certainly possible that would take account of the actual day of birth. Moreover, they should recognise that 1 January is not at the opposite end of the year to 31 December, but rather those days are adjacent - this is the domain of circular statistics (also called directional statistics). Note that the chi-squared goodness of fit test treats month as nominal data, so lacks any concept of ordering of months at all - not only is the subtle point that January is next to December missed out, so is the more obvious fact that January is next to February.
There is another issue with binning by month. If you find a significant result because, say, March and November are overrepresented while May and January are underrepresented, it is difficult to interpret that meaningfully. I suspect this relates to the underlying purpose of your investigation: it's probably not month-to-month variation you're interested in.
Relative age effect and the problem with three month windows
I thought I should say something about why time of year might matter for birthdays of professional sportspeople - at youth level it can be advantageous to be one of the older people in your age category. So what you are investigating isn't a completely silly idea - it is a well-studied phenomenon in academia and sports science called the relative age effect - though your sample size may be too low to detect such an effect even if it exists (this is the problem of statistical power).
I suggested months as you should have enough of a sample size to make a chi-squared test feasible (I imagine your expected frequencies will be at least 5 in each month) and months are a pretty objective thing to classify by.
An issue with sorting into three month windows is that it introduces some subjectivity - do you take January to be part of the window from January to March, or from December to February, or from November to January? It would be tempting to choose in such a way as to maximise the discrepancy between observed and expected births.
Suppose that in youth competition, someone born in September will be the youngest in their age category while someone born in August will the oldest, and you wonder whether this confers an advantage that might impact whether they transition to professional status, then you might just want to compare two six month windows - in my example, September to February versus March to August. You can then see whether being one of the older competitors in your age band as a youth competitor is associated with becoming a professional boxer - though this is subject to various caveats and can't prove causation. What's important is there was an objective justification for the selection of the six month windows, rather than selecting them based on the data. This could be done as a basic chi-squared goodness of fit test with two cells in your table and hence one degree of freedom. 
