Summary: Confidence intervals provide a range of parameter values that would not be rejected if they were tested as null hypothesis values. Their length also signifies the precision of estimation. Fixed width confidence intervals are constructed to control the precision of estimation and, at the same time, to maintain a coverage probability close to the nominal value in the presence of unknown nuisance parameters.
We investigate the ability of triple sampling fixed width confidence intervals to detect shifts in the mean of the normal distribution. Fixed sample size confidence intervals are also evaluated. Operating characteristic curves are generated to compare the performance of the fixed precision confidence intervals for both sampling methods. The results indicate that triple sampling confidence intervals are more capable of detecting shifts in the normal mean than fixed sample size confidence intervals. It is suggested that triple sampling techniques merit more serious consideration in applications.