Confidence Interval
A confidence interval provides a range of values that is likely to contain the true population parameter.
What is a confidence interval?
A confidence interval is a statistical range used to estimate an unknown population parameter, such as a mean or proportion, based on sample data. It reflects the uncertainty inherent in sampling.
Confidence interval formula
For a population mean using the normal distribution, the confidence interval is calculated as:
Confidence Interval = x̄ ± Z × (σ / √n)
Example
Sample mean (x̄) = 50
Standard deviation (σ) = 10
Sample size (n) = 100
Confidence level = 95%
→ Confidence Interval = [48.04 , 51.96]
Standard deviation (σ) = 10
Sample size (n) = 100
Confidence level = 95%
→ Confidence Interval = [48.04 , 51.96]
How to interpret a confidence interval
A 95% confidence interval means that if the sampling process were repeated many times, approximately 95% of the calculated intervals would contain the true population parameter.
What affects the width of a confidence interval?
- Larger sample sizes result in narrower intervals
- Higher confidence levels result in wider intervals
- Greater variability increases interval width
Why are confidence intervals important?
Confidence intervals are widely used in statistics, data science, research, and quality control to quantify estimation uncertainty and support decision-making.