Confidence Interval Math

When determining the confidence interval for a sample of data, 6 values are needed:

  1. X = sample mean
  2. N = sample size
  3. s = √[ ∑ (X-M)2 / (N-1)]  where s = the sample standard deviation and X = each data value
  4. sm = s / √(N) where sm is the standard deviation of M
  5. df = N-1 (df = degrees of freedom)
  6. t= t-value obtained from a t-table according to confidence interval

This is a portion of a t-table from which the t-value can be found using the degrees of freedom (df) and the confidence interval (i.e. Use the 0.10 column for a 90% confidence interval and the row that correlates with each respective degrees of freedom).


Statistical Methods to Find the Confidence Interval:

  1. Take a random sample from a population

  2. Find the mean of the sample (M)

  3. Solve for s  and sm using the equations above

  4. Find the t-value using the t-table which can be found on several sites on the Internet.