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What is Confidence Interval mean?
In statistics, a confidence interval (CI) is a type of estimate computed from the observed data. This gives a range of values for an unknown parameter (for example, a population mean). The interval has an associated confidence level chosen by the investigator. For a given estimation in a given sample, using a higher confidence level generates a wider (i.e., less precise) confidence interval. In general terms, a confidence interval for an unknown parameter is based on sampling the distribution of a corresponding estimator.
This means that the confidence level represents the theoretical long-run frequency (i.e., the proportion) of confidence intervals that contain the true value of the unknown population parameter. In other words, 90% of confidence intervals computed at the 90% confidence level contain the parameter, 95% of confidence intervals computed at the 95% confidence level contain the parameter, 99% of confidence intervals computed at the 99% confidence level contain the parameter, etc.
The confidence level is designated before examining the data. Most commonly, a 95% confidence level is used. However, other confidence levels, such as 90% or 99%, are sometimes used.
Factors affecting the width of the confidence interval include the size of the sample, the confidence level, and the variability in the sample. A larger sample will tend to produce a better estimate of the population parameter, when all other factors are equal. A higher confidence level will tend to produce a broader confidence interval.
Another way to express the form of confidence interval is a set of two parameters: (point estimate – error bound, point estimate + error bound), or symbolically expressed as (–EBM, +EBM), where (point estimate) serves as an estimate for m (the population mean) and EBM is the error bound for a population mean.
The margin of error (EBM) depends on the confidence level.
A rigorous general definition:
Suppose a dataset x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} is given, modeled as realization of random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}} . Let θ {\displaystyle \theta } be the parameter of interest, and γ {\displaystyle \gamma } a number between 0 and 1. If there exist sample statistics L n = g ( X 1 , … , X reference
Posted on 09 Nov 2024, this text provides information on Miscellaneous in Electronics related to Electronics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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