A confidence interval is a range of values that is used to estimate an unknown population parameter with a certain degree of confidence, based on a sample from that population. It is a statistical tool that helps us to make inferences about the population based on the information we have from the sample.
In other words, a confidence interval provides a range of values within which we believe the true value of a parameter lies with a certain level of confidence. This level of confidence is typically expressed as a percentage, such as 95% or 99%.
For example, let’s say we want to estimate the average height of people in a certain population, but we cannot measure the height of everyone in that population. Instead, we take a random sample of people and measure their height. Based on that sample, we can calculate a confidence interval for the true average height of the population. If we calculate a 95% confidence interval, it means that we are 95% confident that the true average height of the population falls within the calculated range.
The confidence interval is based on the sample size, the variability of the data, and the desired level of confidence. A larger sample size generally results in a narrower confidence interval, while a higher level of confidence generally results in a wider interval.
In summary, a confidence interval is a statistical tool that allows us to estimate an unknown population parameter with a certain degree of confidence based on a sample from that population. It is an important concept in statistical inference and helps us to draw conclusions about a population from a sample.
There are two excellent step by step videos by Brandon Foltz on YouTube in how to derive and interpret the confidence intervals. First video is when the population deviation is known and second video is for when the population deviation is unknown.
Before the confidence interval video, watch the standard error of the mean video.