A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be $0\mathrm{.}16$ centimeters in diameter. The variance of the bolts should be $0\mathrm{.}03.$ A random sample of $20$ bolts has an average diameter of $0\mathrm{.}17cm$ with a standard deviation of $0\mathrm{.}2969.$ Can the manufacturer conclude that the bolts vary by more than the required variance at $=0\mathrm{.}01$ level?

Step $3$ of $5$: Determine the value of the test statistic. Round your answer to three decimal places.