MathLiveConfidence interval for a mean (t-interval)
Gives a range that contains the population mean with a chosen confidence level when the population standard deviation is unknown and is estimated by the sample standard deviation. It relies on the t distribution with n-1 degrees of freedom and is used for small or moderate samples from an approximately normal population.
\bar{x} \pm t_{\alpha/2,\,n-1}\,\frac{s}{\sqrt{n}}What the symbols mean
| sample mean | |
| critical value of the t distribution with n-1 degrees of freedom leaving α/2 in each tail | |
| sample standard deviation | |
| sample size | |
| significance level, so the confidence level is 1-α |
About this formula
- FieldStatistics
- TopicConfidence intervals
- LevelUniversity
- Also calledt confidence interval, confidence interval for the mean unknown variance, student t interval, t interval for mean, mean confidence interval small sample, CI for mean with sample standard deviation
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