Not sure what statistical analysis to perform

Hi guys,

This may be an easy question and apologies if it's in the wrong forum, but it's uni-level stats so I figured I'd put it in here.

I'm really stumped as to how to approach the following: I have a data set and it says "it is believed that the true mean value for one concentration is given by a weighted average of the true concentrations found at other locations".

I have alot more info but I'm trying to do this myself so I'm just after a gentle nudge in the right direction, rather than a step-by-step guide.

I'm thinking that since the two concentration sets have different n's, I need to take this into account to work out the weighted average. So say 1 is the first concentration discussed, 2 is one of the true concentrations with n=6 and 3 is the other true concentration where n=5, will it be something like the mean of 1 = (6/11)*mean of 2 + (5/11)*mean of 3? So I'm weighting those concentrations based on how many I have in the sample? And then just do a t-test where H0 = that being true and H1 = that being false but two-sided.

I really hope this makes sense, the more I read the question the more confused I get!