Question: Physical Sciences The lifetime of a fuel rod in a commercial light-water nuclear reactor is related to the internal pressure. Typically, a fuel rod lasts for 36 months, and one-third of all fuel rods are replaced each year during a plant shutdown. A new type of fuel rod includes a gas-relief capsule and is designed to last longer. Independent random samples of the two types of fuel rods were obtained, and the lifetime of each (in months) was recorded. The summary statistics are given in the following table.
Assume the underlying populations are normal and the variances are equal.
a. Conduct the relevant hypothesis test to determine whether the new fuel rod does last longer. Use a = 0.01.
b. Construct a 99% confidence interval for the difference in population mean lifetimes. Does this confidence interval support the hypothesis test conclusion in part (a)? Explain.