Sample Size, Error Rate, Minitab

Robin,

A couple of thoughts for you.... 

The power/sample size calculation that you used is specific to the 2-sample t which means that for that sample size and that power you will be able to see a difference in the average value between the two groups of 0.06.  It doesn't seem from your write up that this is going to have much significance for your problem...

Since the area you are most concerned about is whether the error rate at the branch is representative of all branches, you might want to start at the data from the distribution center.  Gather error rate and volume data for each of the branches and use a Chi Squared Contengency Table to test the hypothesis that the error rate is the same across the sampled branches.  As for sample size here, one of the limitations of the contingency table is that you have to have at least 5 errors from each branch so you will need to ensure that your samples are high enough from each branch to yield at least 5 errors.  The tool does not require that you have an equal number of samples from each branch as long as you yield at least 5 errors...

When you do this study you should also evaluate the types of errors you find...  This is important because one of the issues you need to consider is whether your data associated with the target branch is stratified or has a significantly different mix of errors than the other branches.  A contingency table will help you evaluate this but may require a larger sample to yield the necessary 5 for each cell...

You also need to consider how the error rate changes over time.  I assume that you are using a control chart (P chart) for this...

Hope this helps...

Best Regards,

Bob J