Assessing quality of a fixed sample size with limited information about full set Given the level of this site these are probably intolerably newbie questions, but here goes...
So I'm studying the cost of public transport in a given city.  I have access to data from a hopefully reasonably random survey of the weekly commuting habits of about 60,000 people, and I know the city has about 1,350,000 weekly public transport users.


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*Assuming the distribution of fares is the same for both my sample $n$ and the population, can I simply ignore the size of the population and assert an error bound of $B = \sqrt{1/n} = 0.4\%$?  That is, if (say) 10.0% of my sample pay 50 dollars per week, can I assert that $10.0\pm0.4\%$ of the general population do?

*I don't have access to any fare data for the entire population, but I do know the distribution of travel modes (bus, train, etc) for both sample and population.  How can I compare the two to judge if my sample is representative?  Note that there are only ~4 data points (different modes) and they do not follow any known distribution.
 A: 1.
Assuming you have a fair and correct sample of the population, you can use that error bound (or use something like variance or standard deviation to calculate an error rate). However, there's something to say for the comments of StasK. Self-selection though an internet ad (which in essence it is) can lead to serious bias.

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*Internet penetration of your area. Certain European countries have very high penetration percentages (high 90s) so there it won't matter, but otherwise you quickly have a bias in it.

*People who are willing to click on such a banner (probably something with age and computer literacy of the sample)

*people who want to calculate their fare online (rich people might not care likewise for business travelers, frequent travelers might know it already)

2.
Not really. You can tell if the sample uses the same modes of transport as the population, but that is where it ends. The comparison is simply the percentages of modes of transport. Nothing fancy needed.
The representation of a sample will be more detailed. Think about critical information that shapes your population. Age distribution, average cost, miles traveled etc.
It's not that bad if you don't have all that information (some can be found in secondary sources such as annual reports). But do mention limitations of your research and the assumptions you made. Making assumptions (assuming the sample is representative) is part of research.
