Confidence Interval
for a
Population Mean

where and
with n-1 degrees of freedom.

Notes:

• The above confidence interval may be conveniently represented by its lower and upper limits as follows
  
  
  Note that when the degrees of freedom is sufficiently large (in excess of 30), we can approximate the t percentile in the above confidence interval by the corresponding standard normal percentile. This approximation is usually applied when the required t percentile cannot be found directly from statistical tables.
• When the population variance is known (and assuming normality), use the confidence limits
  
  where
  
  
  
• When n is sufficiently large, we can relax the assumption of normality and obtain approximate confidence limits by using either those given in the preceding item or those given below (the choice depends on whether you know the population variance or not)
  
  
  
• In case you are wondering, the confidence interval given at the top of this page follows from
  
  
  and
  
  
  

Examples:

• See Examples 6 and 7 in Johnson and Bhattacharyya (1996), pp. 322-324.