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How to Calculate Confidence Limits

Confidence intervals are a widely-used statistical measure that calculates the reliability of an estimate of a parameter. The standard confidence interval is 95 percent. In a 95 percent confidence interval, there is a 95 percent chance that the value of the parameter lies between the upper and lower confidence limits of the interval.

Instructions

- 1
  Calculate the mean (m), variance (s^2) and sample number (n) of the random variable (X). The sample mean (X bar) also has a normal distribution with mean (m), but with variance (s^2/n).
- 2
  Calculate your "Z" value. The "Z" value for a 95 percent confidence interval is always 1.96. To find the Z value for other confidence intervals use a Z-score chart.
- 3
  Substitute your values into the following equation:
  
  Z = (x bar) - (m) / (s^2/n).
- 4
  Re-arrange the equation as follows to find (x bar):
  
  (x bar) = Z(s^2/n) + (m)).
- 5
  Calculate your confidence limits by adding and subtracting Z(s^2/n^0.5) from your sample mean (x bar).

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