• Describe a population and sample of interest.
• Use technology to find sample statistics from a sampling distribution.

Inferential Statistics

One of the goals of statistical inference is to draw a conclusion about a population on the basis of a random sample from the population.

We need to understand how much random samples vary and how they relate to the population. Our ultimate goal is to create a probability model that describes the long-term behavior of sample measurements. We use this model to make inferences about the population.

Sampling Distribution of a Statistic

Let’s use this new vocabulary to rephrase what we already know at this point:

• When we make inferences, a parameter is typically not known because it is impossible or impractical to gather data from everyone in the population. (Note: In order to investigate how statistics relate to parameters, we used a known parameter in our example. This is the first step in creating a probability model. However, when we make inferences in real life, we use a statistic to draw a conclusion about an unknown parameter.)
• We make an inference about the population parameter on the basis of a sample statistic.
• Statistics from samples vary.

sampling distribution of a statistic

The sampling distribution of a statistic is a probability distribution that describes the long-term behavior of the statistic.

An approximate sampling distribution can be constructed from a large number of samples of size [latex]n[/latex] from a given population. So, to create a probability model that describes the long-term behavior of the statistic, we can collect a few random samples to make a distribution of the sample statistic, and we can use technology to help us create such a distribution.