A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the $445$ gram setting. It is believed that the machine is underfilling the bags. A $13$ bag sample had a mean of $444$ grams with a standard deviation of $12.$ A level of significance of $0\mathrm{.}01$ will be used. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.