Savings would be achieved if the combined costs of (1) examining the sample and (2) projected losses due to undetected errors on invoices not examined are less than the administrative cost of examining all invoices.
Savings could be had if the sample was examined and errors are detected. 
mnli hypothesis: Savings could be had if the sample was examined and errors are detected.  premise: Savings would be achieved if the combined costs of (1) examining the sample and (2) projected losses due to undetected errors on invoices not examined are less than the administrative cost of examining all invoices.