Confidence Interval Calculator for a Single Sample (Z-Statistic)
This confidence interval calculator provides full details of the calculation, including sample mean, population standard deviation, and the confidence interval using the z-distribution.
Further Information
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. When the population standard deviation is known, we use the z-statistic (normal distribution) to calculate the confidence interval.
When to Use
- Single sample data
- Population standard deviation is known
- Sample size is large (typically n ≥ 30)
- Data is normally distributed or n is large enough for CLT to apply
Equation
CI = M ± (zα/2 × SE)
Where M is the sample mean, zα/2 is the critical z-value for the desired confidence level, and SE is the standard error (σ/√n).
Standard Error
SE = σ / √n
Where σ is the known population standard deviation and n is the sample size.