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 them that will vote for Joe.
The sample is the 2000 registered voters that were polled, and
the statistic is the percentage of them that will vote for Joe.
You can tell Joe that approximately 56% of all registered voters
will vote for him.
Ex. In a Statistics class of 40 students, 24 had a credit card
The statement "60% of the students in this Statistics class
had a credit card with them" is a descriptive statement.
The population is the 40 students in this Statistics class. The
60% represents a parameter.
The statement "60% of the students in all classes have a
credit card with them" is an inferential statement. The 40
students in this Statistics class represent a sample of students
in all classes. The 60% represents a statistic.
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