# Statistics - Statistical Inference

## Statistical Inference

Using data analysis and statistics to make conclusions about a population is called statistical inference.

The main types of statistical inference are:

• Estimation
• Hypothesis testing

## Estimation

Statistics from a sample are used to estimate population parameters.

The most likely value is called a point estimate.

There is always uncertainty when estimating.

The uncertainty is often expressed as confidence intervals defined by a likely lowest and highest value for the parameter.

An example could be a confidence interval for the number of bicycles a Dutch person owns:

"The average number of bikes a Dutch person owns is between 3.5 and 6."

## Hypothesis Testing

Hypothesis testing is a method to check if a claim about a population is true. More precisely, it checks how likely it is that a hypothesis is true is based on the sample data.

There are different types of hypothesis testing.

The steps of the test depends on:

• Type of data (categorical or numerical)
• If you are looking at:
• A single group
• Comparing one group to another
• Comparing the same group before and after a change

Some examples of claims or questions that can be checked with hypothesis testing:

• 90% of Australians are left handed
• Is the average weight of dogs more than 40kg?
• Do doctors make more money than lawyers?

## Probability Distributions

Statistical inference methods rely on probability calculation and probability distributions.

You will learn about the most important probability distributions in the next pages.