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"When asked what they would use if they were marooned on an island with only one choice for a pain reliever, more doctors chose A than B, C or D."

Is this conclusion drawn from population or a sample?

I am confused here because how do we know if on an island there were all the doctors that they could've asked the question?


"25% of the cars sold in US in 1996 were manufactured in Japan."

Even for this statement how do we know if it was drawn from sample or population?

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  • $\begingroup$ The answers to such questions depend on what inferences you will make. You haven't provided any inferences (or even conclusions, for that matter): you only quote descriptive statistics. From this perspective, your question doesn't seem to be answerable. Would you like to edit the post to clarify what you would like to know? $\endgroup$ – whuber Aug 11 '18 at 20:11
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First Scenario

Your first example talks about "doctors". The set "doctors" includes all living doctors, all dead doctors, all retired doctors, all around the world. So if somebody wants to make a statement about doctors - they have to use a sample of it.

Even if the statement only talks about US based still practicing doctors who are familiar with the pain-relievers A,B,C,D - it would still probably be based on a sample, unless someone actually surveyed every such doctor.

Second Scenario

The second example is probably based on the whole population because it sounds like it talks about all the cars sold in US in the year 1996. It's possible that somebody has all the records of cars sold in the US in that year. So in this case they would have the whole population.

Additional Example

Here is one additional example that should help: You are a teacher and you want to measure the difference in height between boys and girls in your class. Let's think about population and sample:

  1. Population: your class is the population and you can say "boys in my class are on average 5cm higher than girls". This would be statement of fact after measuring the heights. No confidence intervals, p-values or other uncertainty estimates would be needed.
  2. Sample: your class is a sample of all the boys and girls that could possibly attend your class. Then you could say that the best estimate you have about the difference of height between boys and girls is 5cm. But you are aware that if other boys and girls attended your class it wouldn't be 5cm and there is even a chance that girls would be higher. And you can produce various uncertainty measures.

Summary

In general statistics is much more frequently concerned about making statements from a fixed sample and seeing how well it applies to the population from which the sample was drawn.

You talk about population when you have every member of it measured. And you talk about sample when you measure only some members and try to extend your observations to the broader population.

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  • $\begingroup$ I don't think the question is answerable: I stated why in a comment to the question itself. The issue isn't whether a statistic is "based on" a "sample" or a "population," because a set of doctors or set of cars may equally well be viewed as a population for one purpose and a sample for another purpose. $\endgroup$ – whuber Aug 11 '18 at 20:12
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    $\begingroup$ @whuber This is what I tried to get at with the "classroom" example: same class of pupils and one can talk about only pupils at that class, or can try to reason about the larger population based on the sample that is the class. But I agree with you completely - the question is at best poorly worded. $\endgroup$ – Karolis Koncevičius Aug 11 '18 at 20:34
  • $\begingroup$ I see that you made that point well in your "additional example," +1. $\endgroup$ – whuber Aug 11 '18 at 20:37

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