GlenCalc

Confidence interval calculator

Enter your sample results to get the range that, at the chosen confidence level, is expected to contain the true value.

Your answer

95% confidence interval47.441476 to 52.558524
Margin of error2.558524
Critical t (df = 39)2.0227

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How we worked it out

Updated as you change the numbers.

  1. Margin = critical value × SD ÷ √n; interval = mean ± margin.
  2. The t distribution is used when the SD comes from the sample, which widens small-sample intervals.

Method and assumptions

For a mean, the interval is x̄ ± t* × s ÷ √n, with t* from the t distribution with n − 1 degrees of freedom (or z* if the population SD is known). For a proportion it uses the normal approximation p ± z* √(p(1 − p) ÷ n).

Questions

What is the 95% confidence interval for a mean of 50, SD 8, n = 40?

About 47.44 to 52.56.

Sources

Method and figures checked on . Every worked answer on this page is covered by an automated test. Found a mistake? Tell us.

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