The manufacturer of a popular antibiotic must ensure that each 5-mL dose contains 250 milligrams (mg) of the active ingredient. It is also essential that the variance of the amounts of active ingredient per dose be less than 0.3. For testing purposes, a random sample of 269 doses is taken, and the standard deviation of the amounts of active ingredient per dose in the sample is found to be 0.5mg. Does the evidence support the claim that the variance is within the necessary bounds, at the 0.01 level of significance