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Population and Sample

The major use of inferential statistics is to use information from a sample to infer something about a population.

A population is a collection of data whose properties are analyzed. The population is the complete collection to be studied, it contains all subjects of interest.

A sample is a part of the population of interest, a sub-collection selected from a population.

A parameter is a numerical measurement that describes a characteristic of a population, while a sample is a numerical measurement that describes a characteristic of a sample. In general, we will use a statistic to infer something about a parameter. 

Ex. Joe D. Politician is running for President. He calls you on the phone and asks you to find out what percentage of the registered voters in the country will vote for him. There are a few things you could try.

Option I : Call all registered voters on the phone and ask them who they will vote for.

Although this would provide a very accurate result, it would be a very tedious and time consuming project. All registered voters represent the population of interest here, and a better approach would be to use a sample. 

Option II : Call 4 registered voters, 1 in each time zone, and ask them who they will vote for.

Although this is a very easy task, the results would not be very reliable. To use a sample to make inferences about a population, the sample should be representative of the population. How likely is it that these 4 registered voters would represent the population of all registered voters? Not very! The sample needs to look just like the population, but smaller.

Option III : Somewhere between Option I and Option II.

We want to use a method that will be easier than Option I, but more reliable than Option II.

So, you randomly select 2000 registered voters and poll them. 1,120 (56%) tell you that they will vote for Joe. 

The population of interest here is all registered voters, and the parameter is the percentage of...