Final answer:
The procedure that gives the least assurance for the existence of investment balances is the examination of canceled checks, as it confirms payment but not current possession.
Step-by-step explanation:
In a manufacturing company, when auditing the existence of the general ledger balance of investment in stocks and bonds at the audit date, the procedure that provides the least assurance is the examination of canceled checks issued in payment of securities purchased. This is because while such examination confirms payment was made, it does not necessarily provide evidence that the company possesses the stocks and bonds currently. In contrast, procedures like confirmation from the broker, actual inspection and count of the securities, and vouching all changes during the year to brokers' advices and statements give more direct evidence regarding the existence of these investments as of the audit date.