Testing Hypotheses
About a
Population Mean

where

Notes:

• When the degrees of freedom is sufficiently large (in excess of 30), we can approximate the t percentiles by the corresponding standard normal percentiles if necessary.
• When the population variance is known (and assuming normality), use the following test statistic
  
  
  instead of the one given earlier and replace the t percentiles which define the various critical regions by the corresponding standard normal percentiles.
• When n is sufficiently large, we can relax the assumption of normality and obtain approximate statistical tests. The critical regions for the various approximate tests remain the same as those for the known variance case and the test statistic is one of the two given earlier (the choice depends on whether you know the population variance or not).

Examples:

• See Examples 8, 9 and 10 in Johnson and Bhattacharyya (1996), pp. 334-338.