Confidence interval for a mean
Compute the confidence interval and margin of error for a sample mean, from the sample size, standard deviation and confidence level.
- Confidence interval
- Margin of error
- Standard error
- Critical value
The interval
Confidence interval97.060056 to 102.939944≈
Margin of error± 2.939944≈
Lower bound97.060056≈
Upper bound102.939944≈
How it is built
Sample mean100
Sample size100
Standard error1.5s / √n
Critical value1.959963≈the z for 95% two-sided
Confidence level95%
What this assumes
Critical valueNormal (z), not Student tfor a small sample the t distribution is wider and this interval is too narrow; the difference is under 3% by n = 30 and under 1% by n = 100
Interpretation95% of such intervals contain the true meannot "a 95% chance the mean is in this interval": the mean is fixed, the interval is what varies
SamplingIndependent and randomno arithmetic can rescue a biased sample