The owner of an ice cream parlor is concerned about consistency in the amount of ice cream his servers put in each cone. He would like the variance of all such cones to be no more than .25 square ounces. He decides to weigh each double-dip cone just before it is given to the customer. For a sample of 20 double dip cones, the weights were found to have a variance of .48 square ounces. Assume that the weights of all such cones are (approximately) normally distributed.
a. Construct the 99% confidence intervals for the population variance and the population standard deviation.
b. Test at a 1% significance level whether the variance of the weights of all such cones exceeds .25 square ounce.