A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is .3 inches. A sample of 25 pipes was taken. The average length in the sample was 15.95 inches with a variance of .4 inches.

a. Construct a 95% confidence interval for the population variance.

b. Test whether or not the population variance equals.3 inches at the 5% level ofsignificance. Please provide a detail explanation of it.