The problem I'm trying to solve goes like this:
There are 1000 phones produced at a factory, which wants to take a sample of 20 phones to inspect their quality. Why would taking the last 20 phones be a bad idea?
The answer I put was something along the lines of "taking the last 20 phones ensures that the sampling frame of the statistic is only 20 phones instead of the ideal 1000, which can result in bias".
However, after submitting the answer, I'm increasingly unsure that my answer was correct. Can somebody explain this problem to me?
Sampling a population does not result in bias, so long as you have chosen a representative sample. A random sample of 20 phones out of 1000 is not biased simply because we haven't tested all 1000. The random sampling method doesn't result in bias because there's no characteristic of the manufacturing process that's linked to the sample selection in any way.
On the contrary, if you take only the last 20 phones, you may have introduced bias if there are time-dependent effects on quality. Perhaps the factory machines accumulate wear and produce lower quality phones over time, or maybe the less-skilled night shift came on to produce the final batch of phones. If there is any relationship between production order and quality, sampling only phones from the very end of the production run will not give a representative sample over the whole batch. If there is a relationship between quality and time, choosing a set that is biased in time will produce a set that is biased in quality.