Confidence Interval Calculator for a Single Sample (T-Statistic)
This confidence interval calculator provides full details of the calculation, including sample mean, sum of squares, standard deviation, and the confidence interval using the t-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 unknown (which is typically the case), we use the t-statistic to calculate the confidence interval.
When to Use
- Single sample data
- Population standard deviation is unknown
- Sample size is small (typically n < 30)
- Data is approximately normally distributed
Equation
CI = M ± (tα/2 × SE)
Where M is the sample mean, tα/2 is the critical t-value for the desired confidence level, and SE is the standard error (s/√n).
Standard Error
SE = s / √n
Where s is the sample standard deviation and n is the sample size.