Q:

Testing whether the mean of a group is different from the mean of the entire sample

I have the mean and standard deviation of a large sample (30k obs) and the mean and std of a subsample (2k obs). The means are percentage figures (i.e. between 0 and 100% and hence not a normal variate). Also the means are not independent, since one is based on a subsample from the other.  
Despite seemingly a harmless question, I could not find an appropriate testing procedure. Any ideas on how to test whether the mean of the subsample is different to the mean of the entire sample are much appreciated.

A:

Instead of testing subsample vs. whole sample, test subsample vs. those not in subsample. Then you can test the difference in proportions with a chi square test, since it sounds like they must be being tested on some other categorical variable or, if you prefer, you can do logistic regression with the percent agreement thing (whatever variable that is) being the dependent variable and "being in the subsample" as the IV.
Logistic regression treats one variable as dependent and the other as independent, while chi-square treats the two variables equally. Also, logistic regression would allow you (if you have data) to add other variables to the equation.  
Response to comment
Since the whole sample = 30,000 and 50% have whatever it is, that means that divides 15,000 and 15,000. The subsample is 2,000 with 45% having whatever it is, so that's 900 and 1,100. That means those NOT in the subsample are (15,000-900) and (15,000 - 1,100) = 14,100 and 13,900. Now you can do chi square test on the table:
              Yes      No
Sub           900     1,100
Not sub    14,100    13,900

