To find an interval estimate for the parameter of the Bernoulli or the Poisson distribution usually requires the sample size to be large so that the normal approximation may be used. Small sample intervals have been proposed earlier, but the procedures have required tables and are inexact. In this note we give a simple procedure for finding a small sample confidence interval with minimum interval width. We also give a geometric interpretation to the minimization problem. Data Abstract Understanding and monitoring customer needs and satisfaction are crucial requirements of quality management.
Many organizations collect frequent customer satisfaction data over time using customer surveys.
A logical yet infrequently used means of monitoring these data is with process control charts. Control charts provide managers with a mechanism for scanning the external and internal environments for changes in customer satisfaction levels. Traditional Shewhart charts need to be modified, however, to monitor categorical or ordinal customer survey data. Using data from a major hospital, we show how blindly applying traditional Xbar charts to ordinal survey data can lead managers to erroneous conclusions about the level of customer satisfaction. We also discuss two alternative charts that are more appropriate for survey data.