# Confidence interval

Last updated August 14, 2023

## What is a confidence interval?

A confidence interval (CI) refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. The two most frequently used confidence levels are 95% and 99%. This implies that when using a 95% confidence level, for instance, the estimate will fall within the interval 95 out of 100 times.

## How to calculate the confidence interval?

The confidence interval is calculated using a statistical formula that takes into account the sample size:

Confidence Interval (CI) = Sample Mean ± Margin of Error (Standard deviation / √Sample Size)

Confidence interval (CI) = *x̄ * ± Z(S ÷ √n).

## Why use confidence intervals?

Confidence intervals are an important tool that allows us to estimate the range of values in which the true population parameter is likely to fall. They are used to assess the precision of an estimate and provide a measure of probability/certainty. Additionally, confidence intervals are useful for comparing groups and determining if their parameter estimates overlap or are significantly different.

## What is the difference between confidence intervals and confidence levels?

Both statistical concepts are used to describe the accuracy and precision of an estimate.

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. For example, a 95% confidence interval for the mean weight of a certain population might be from 60kg to 80kg. This means that if the same population was sampled repeatedly, then 95% of the intervals calculated would contain the true mean weight of the population.

A , on the other hand, is the percentage of probability that the confidence interval would contain the true population parameter when you draw a random sample many times.