Assessing effect of sample in its population I have population of 200 people with their BMI . I want to remove 30 people of similar characteristics from the group and see if that makes any statistical difference on BMI of population(now 170). I am wondering what test would be appropriate here. Any theoretical/programming link will be appreciated.
 A: The Wilcoxon rank sum test might work if you want to test the effect on the location (mean/median) of the BMI rather than scale (variance etc).
Example: consider the Mississippi adult BMI data from 1990 and 2003 data, as described here.  Using R to simulate those (just for demonstration purposes) ...
bmi.1990 = rnorm(1498,25.4,4.88)
bmi.2003 = rnorm(4212,27.7,6.12)

Now using R to test the hypothesis that, overall, the BMI hasn't gone significantly up or down between those time periods:
wilcox.test(bmi.1990,bmi.2003)

    Wilcoxon rank sum test with continuity correction

data:  bmi.1990 and bmi.2003
W = 2443871, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

That tiny p-value is strong evidence against the hypothesis of unchanged BMI.  In other words, it has changed.
I can't quite tell if you genuinely wish to compare the original 200 against the reduced 170 (as you seem to imply), or the special 30 against the 170 remainder.  If the latter, then it's a test like the one shown above.  If the former, then it's like a test of (say) bmi.1990 against the union of bmi.1990 and bmi.2003.
