Title: Confidence interval - Wikipedia
Headings: Confidence interval
Confidence interval
Contents
Conceptual basis
Introduction
Meaning and interpretation
Misunderstandings
History
Philosophical issues
Relationship with other statistical topics
Statistical hypothesis testing
Confidence region
Confidence band
Basic steps
Significance of t-tables and z-tables
Example
Statistical theory
Definition
Approximate confidence intervals
Desirable properties
Methods of derivation
Summary statistics
Likelihood theory
Estimating equations
Hypothesis testing
Bootstrapping
Examples
Medical examples
Theoretical example
Alternatives and critiques
Comparison to prediction intervals
Comparison to Bayesian interval estimates
Confidence intervals for proportions and related quantities
Counter-examples
Confidence procedure for uniform location
Confidence procedure for ω2
See also
Confidence interval for specific distributions
References
Bibliography
External links

Content: 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. Many confidence intervals are of the form
( t − c σ T , t + c σ T ) {\displaystyle (t-c\sigma _ {T},t+c\sigma _ {T})}
, where
t {\displaystyle t}
is the realization of the dataset, c is a constant and
σ T {\displaystyle \sigma _ {T}}
is the standard deviation of the dataset. Another way to express the form of confidence interval is a set of two parameters: (