Assuming you're particularly interested in whether the sample mean is too different from the population mean to be consistent with random selection from the population, and you have the complete population you might look at the distribution of sample means for samples of size 11 from that population.
This is the null distribution for the test statistic (the sample mean) for the hypothesis that the sample is drawn at random.
You then see where the sample mean falls in the null distribution (specifically find the proportion of results at least as extreme as your sample proportion).
Here's an illustration for data somewhat similar to yours:
For a one-tailed test you compute the proportion whose means are at least as far from the population mean in the specified direction as your sample is (that's what's calculated above). If your alternative is two-tailed, you also need to identify what you mean by 'at least as extreme in the other direction' (it might be 'the mean is at least as far below', or it might simply be that you're after a similarly extreme quantile in the other direction -- which would result in doubling the tail proportion). In the two-tailed case, it may be easier to begin by thinking about a suitable form of rejection rule and then adjust your rejection rule to the desired significance level.
In either case if the resulting p-value is less than your significance level, you would reject the null hypothesis of random selection from the population.
All of the foregoing assumes that the decision to compare means was not made on the basis of what you see in the sample, but was a comparison that you would want to make before the sample was looked at.
If you want a more general test than a comparison of means, you might look at a similar procedure based off a goodness of fit statistic (but such broadening of the alternatives being considered will usually bring with it a loss of power). If the decision to restrict the comparison to a test of means was based on looking at the data (but you'd still have wanted some comparison), then this option may be about the only reasonable choice.