7.
Product and Process Comparisons
7.3. Comparisons based on data from two processes 7.3.1. Do two processes have the same mean?


Definition of confidence interval for difference between population means 
Given two random samples,
$$ Y_1, \, \ldots, \, Y_N \,\,\,\,\, \mbox{ and } \,\,\,\,\,
Z_1, \, \ldots, \, Z_N $$
from two populations, twosided confidence intervals with \(100(1\alpha)\) % coverage for the difference between the unknown population means, \(\mu_1\) and \(\mu_2\), are shown in the table below. Relevant statistics for paired observations and for unpaired observations are shown elsewhere. Twosided confidence intervals with \(100(1\alpha)\) % coverage for \(\mu_1  \mu_2\):


Interpretation of confidence interval  One interpretation of the confidence interval for means is that if zero is contained within the confidence interval, the two population means are equivalent. 