Confidence Intervals
In statistics, a confidence interval (CI) is a range of values that is estimated to contain the true population parameter with a certain level of confidence
In statistics, a confidence interval (CI) is a range of values that is estimated to contain the true population parameter with a certain level of confidence. It is commonly used to estimate the unknown mean or proportion of a population, based on a sample.
To construct a confidence interval, you typically start with a sample from a population. The sample should be selected randomly and should be representative of the population of interest. Next, you calculate sample statistics, such as the sample mean or proportion. These sample statistics serve as estimates for the population parameter.
The confidence interval is calculated by first determining the margin of error. The margin of error depends on two factors: the sampling variability and the desired level of confidence. The sampling variability is influenced by the sample size and the variability in the population. The level of confidence determines the percentage of confidence intervals that would contain the true population parameter if repeated sampling were conducted.
Commonly used levels of confidence are 90%, 95%, and 99%. For example, a 95% confidence interval means that if you were to take multiple samples and construct a confidence interval each time, approximately 95% of those intervals would contain the true population parameter.
Once the margin of error is determined, it is added and subtracted from the sample statistic to establish the lower and upper bounds of the confidence interval. These bounds represent the range of values within which the true population parameter is estimated to fall.
It’s important to note that a confidence interval is an estimate, and there is a chance that the true population parameter might not be within the interval. However, with higher levels of confidence, the chance of the parameter being outside the interval decreases.
Confidence intervals provide a useful way to quantify the uncertainty associated with our estimates. They allow us to not only estimate a population parameter but also understand the range within which this parameter is likely to lie. This information is crucial for making accurate inferences and drawing conclusions from statistical data.
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