Understanding Confidence Intervals | A Statistical Tool for Estimating Unknown Population Parameters

confidence interval

A confidence interval is a statistical concept that provides a range of values within which an unknown population parameter is likely to fall

A confidence interval is a statistical concept that provides a range of values within which an unknown population parameter is likely to fall. It is often used to estimate an unknown population parameter, such as a mean or proportion, based on a sample of data.

In practice, a confidence interval is constructed by determining an estimate of the population parameter from the sample data, along with an associated margin of error. The margin of error is a measure of the uncertainty or variability in the estimate. The confidence interval is then defined as the range of values within the estimate is likely to be found, using a specified level of confidence.

The level of confidence is often expressed as a percentage, such as 95% or 99%. For example, a 95% confidence interval means that if we were to repeatedly sample from the population and construct confidence intervals, we would expect 95% of those intervals to contain the true population parameter.

The formula for calculating a confidence interval varies depending on the parameter being estimated and the distribution of the data. For example, when estimating the mean of a normally distributed population, a common approach is to use the sample mean along with the standard deviation of the sample to construct the interval.

Confidence intervals are widely used in hypothesis testing, as they help determine whether a population parameter is likely to fall within a certain range of values, based on the observed sample. They provide a measure of the precision of an estimate and help researchers make informed decisions about their data.

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