Confidence intervals in simple words
When you measure a sample (a small group) instead of everyone, your answer is only an estimate. A confidence interval is a range that probably holds the true answer for everyone.
The range is your sample result plus or minus a margin of error (how far off the estimate could be). A bigger sample gives a smaller margin. Asking for more confidence, such as 99% instead of 95%, gives a wider range.
Example: 100 apples weigh 150 g on average, and apple weights have a standard deviation (a measure of spread) of 20 g. The standard error is 20 ÷ √100 = 2 g. At 95% confidence the margin is 1.96 × 2 = 3.92 g, so the interval is 146.08 g to 153.92 g.
95% confidence means that if you repeated the whole survey many times, about 95 out of 100 of the ranges you made would contain the true value.
Formula and method
For a mean with known population standard deviation σ, use x̄ ± zσ/√n. For a proportion use the Wilson score interval, which remains between 0 and 1.
Worked example
A mean of 50, known population deviation 10 and sample size 100 give a 95% interval of approximately 48.0400–51.9600.