Statistical Inference

Statistical inference is drawing conclusions about populations using data collected from samples of those populations.

Some important statistical inference methods are:

Confidence Intervals
Confidence intervals are a type of statistical inference where we create an interval using data from a sample and estimate the probability that some population parameter is found within (captured by) that interval.

Intervals are often described in the form "the interval a ± b" (which means the interval from a - b to a + b.)

A level C confidence interval for a parameter is an interval which has a C percent chance of capturing that parameter.

Confidence intervals are often used to estimate:
A population mean.
The difference between two population means.
A population proportion.

Tests of significance
Significance tests are a type of statistical inference where information from a sample of a population is used to assess the validity of a claim made about that population. Significance tests look at the properties of the sample, and work out the probability of obtaining such a sample if a given claim about the population is true. This probability is called the "P-value" of the test.

Tests of significance are often used to assess the validity of claims about:
A population mean.
The difference between two population means.
A population proportion.

A two-sided significance test at significance level α will reject a hypothesis when µo (H0's prediction of µ) falls outside the 1 - α confidence interval for µ.