Can you infer that sample is representative from statistical power? I have travel times for 1000 routes (origin-destination pairs) and I collected about 12 actual travel time samples by driving some of these routes (randomly selected out of the 1000). 
I calculated statistical power of the 12 samples with an online power calculator by using the mean and standard deviation of the 1000 pairs and mean of the sample (alpha = 0.05). 
I got a power of 1 which I read somewhere means that the trend in the population would always be detected (from samples of any size). I then used this as a justification that the 12 samples are representative, and compared it with travel times for the sample routes obtained from other sources. A comparison of observed travel time vs predicted ones.
Is this valid, and is inference of this sort achievable from statistical power? Also considering that observed time is being compared to time predicted from long-term averages (for similar driving conditions), how valid should I consider results of such statistical analyses.
 A: Representative (if that's a concept at all; you may hear the term tossed around, but it means nothing to statisticians) is a function of the design. An example of a representative sample is a simple random sample in which every sample of size 12 out of 1000 is as likely to be drawn as the next (there are ${1000 \choose 12}=1.95\cdot10^{27}$ such samples). An example of a non-representative sample is when you order it alphabetically by the name of the origin point and take the first 12. Power is mostly a function of sample size (and, to the lesser extent, of other design decisions, such as balancing the sample sizes of different treatment groups, or degree of data clustering). So one cannot really inform the other. Power calculations nearly necessarily assume unbiased designs (otherwise, why bother collecting the data if you know that your result is biased).
I don't see any way on earth a sample of size 12 could give a power of 1. I reasonably expect that you plugged the numbers in wrong places in that (unspecified) calculator.
