Ci Interval Calculator

Required for the mean intervals.
Used by the t interval.
Used by the z interval, when sigma is genuinely known.
Used by the proportion intervals.
An alternative to the success count for the Wald and Wilson intervals.
Beta(1,1) is the uniform prior. Only used by the Bayesian method.
Applies the finite population correction when the sample is a large share of the population.
Margin of error
1.959964
Confidence Interval Calculator
Lower limit
48.040036
Upper limit
51.959964
Point estimate
50
Standard error
1
Critical value
1.959964
Confidence level
95 %
Alpha (1 - confidence)
0.05
Width of the interval
3.919928
Finite population correction
1
Interval
(48.040036, 51.959964)
Method
z interval for a mean with a known population standard deviation
Worked out from NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.2 Confidence Limits for the Mean and 4 other sources.
A confidence interval only describes sampling error under its stated model. It says nothing about bias, non-response or measurement error, and the Bayesian mode is only as defensible as the prior you enter.

How this is worked out

4 steps
  1. Standard error = 10 / sqrt(100) = 1.
  2. The 97.5th percentile of the standard normal distribution is 1.9599639845.
  3. Margin of error = 1.9599639845 x 1 = 1.9599639845.
  4. Interval = 50 +/- 1.9599639845 = (48.04003602, 51.95996398).

Results are general information, not financial, tax, legal, medical or engineering advice.