Confidence Interval

Confidence Interval is a statistical concept that is used to estimate the range within which a population parameter is likely to fall. It is a type of interval estimate that is computed from the observed data. The confidence interval provides an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

Definition

A Confidence Interval (CI) is a range of values, derived from a statistical calculation, that is likely to contain the value of an unknown population parameter. The interval has an associated confidence level that quantifies the level of confidence that the parameter lies within the interval. The confidence level is often set at 95%, which means that the interval would contain the true population parameter 95% of the time if the estimation process was repeated a large number of times.

Calculation

The calculation of a confidence interval depends on the statistical distribution that is assumed for the population data. For a normal distribution, the confidence interval for the mean is calculated as:

x̄ ± Z * (σ/√n)

where:

• x̄ is the sample mean
• Z is the Z-score which corresponds to the desired confidence level
• σ is the standard deviation of the population
• n is the sample size

Interpretation

The interpretation of a confidence interval is that if the statistical analysis is repeated many times, then the calculated confidence interval would include the true population parameter in a certain percentage of the times. For example, a 95% confidence interval means that if the analysis was repeated 100 times, then the true population parameter would be within the interval in 95 out of 100 cases.

Limitations

While confidence intervals are a powerful tool in statistics, they have certain limitations. They are based on the assumption that the sample data is representative of the population, which may not always be the case. Also, the width of the confidence interval depends on the sample size and variability in the data, which means that a large sample size or high variability can result in a wide confidence interval.

See Also

• Standard deviation
• Z-score
• Statistical distribution
• Sample size

Confidence Interval Resources
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