Question: 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 ounce. He decides to weigh each double-dip cone just before it is given to the customer. For a sample of 20 doubledip cones, the weights were found to have a variance of .48 square ounce. 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 the 1% significance level whether the variance of the weights of all such cones exceeds .25 square ounce.