The manufacturer of a certain brand of light bulbs claims that the variance of the lives of these bulbs is 4200 square hours. A consumer agency took a random sample of 25 such bulbs and tested them. The variance of the lives of these bulbs was found to be 5200 square hours. Assume that the lives of all such bulbs are (approximately) normally distributed.
a. Make the 99% confidence intervals for the variance and standard deviation of the lives of all such bulbs.
b. Test at a 5% significance level whether the variance of such bulbs is different from 4200 square hours.