In order to ensure that the bolts a machine produces are consistent, the variance of the bolt diameters must be 0.03. Each machine is tested by taking a random sample of 11 bolts produced. The manufacturer finds that the 0.26 centimeter bolts have a standard deviation of 0.1069. Does the manufacturer have evidence at the =0.01 level that the variance of the bolt diameters is different than required? Assume the population is normally distributed.

State the null and alternative hypotheses. Round to four decimal places when necessary.

Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Determine the value of the test statistic and p-value. Round your answer to three decimal places.