99% Confidence Interval Calculator

Your details

Use the z interval when you know the true population standard deviation. Use the t interval (the most common) when you only have the sample standard deviation. Use Proportion for a success count out of a total.
The arithmetic average of your sample (x-bar).
The sample standard deviation. The t interval accounts for the extra uncertainty this introduces.
Number of observations. Needs at least 2 for the t interval (df = n - 1).
Lower boundWide interval
44.9667

The lower limit of the confidence interval

Upper bound55.0333
Margin of error5.0333
Critical value2.7569
Standard error1.8257
2.75690.3% above · Standard deviations from mean

99% CI: [44.9667, 55.0333]

  • The 99% confidence interval runs from 44.9667 to 55.0333, with a margin of error of 5.0333.
  • With 30 observations, the t critical value on 29 degrees of freedom is 2.7569. As n grows, this approaches the z critical value (2.5762).
  • A wider confidence interval means more uncertainty in the estimate. Increasing the sample size is the most reliable way to shrink the margin of error.

Next stepIf the interval is too wide for your purpose, you can estimate the sample size needed to achieve a target margin of error: n = (z* x sigma / ME)^2 for means, or n = z*^2 x p(1-p) / ME^2 for proportions.

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