This is part of a larger question, about sample distribution of means, that I'm having problems understanding, so please bear with me.
If I record the time between planes landing, and have 250 observations, are those 250 observations my "population", or does the term "population" refer to all the values, i.e. if I had sat there till the end of time recording?
I'm assuming its the latter but just want to double check.
To my understanding, you're trying to estimate the population with the sample, because normally you don't have the whole population. For example if you're trying to estimate the average height of all men in the world ever existed, you obviously can't measure every single one of them. But you can take a sample measure, say 1,000,000 men and then you average their height. As the number of samples increases you're approaching the real population.
In your case I guess yes you would have to measure every time interval between planes landing ever in order to get the whole population...So your 250 observations would be the sample I think, if planes still kept landing after your observations :)
Here's another definition of population and sample:
When we think of the term “population,” we usually think of people in our town, region, state or country and their respective characteristics such as gender, age, marital status, ethnic membership, religion and so forth. In statistics the term “population” takes on a slightly different meaning. The “population” in statistics includes all members of a defined group that we are studying or collecting information on for data driven decisions. A part of the population is called a sample. It is a proportion of the population, a slice of it, a part of it and all its characteristics. A sample is a scientifically drawn group that actually possesses the same characteristics as the population – if it is drawn randomly.
The population is the entire group that you are interested in; your sample is a subset of that group.
In your case, of times between planes landing, it is not obvious what the population is, at least, not from what you have told us. If your 250 cases were all the times between landings for one day, and all you were interested in (for some reason) was that one day, it would be the population. Probably that is not the case. But what is your population? All times between landings at that airport for one week? One month? A year? The last 20 years? More than one airport? More than one country? All the airports in the world?
Technically, for inference from a sample to a population to be correct (at least, without extensive complications), you need to have some sort of random sample (there are many types of random sample) of the population. However, people use samples of convenience quite a lot. Often there is no way to get a really random sample; other times, it is technically possible but prohibitively expensive; there can be other problems as well.
