The mean weight of an ordinary key is an important consideration, as most people carry a pocketful of keys. A manufacturer claims that a new process...

The mean weight of an ordinary key is an important consideration, as most people carry a pocketful of keys. A manufacturer claims that a new process produces a lighter and more durable key. Independent samples of both types of keys were obtained, and each key was carefully weighed and its weight (in ounces) was recorded. The resulting summary statistics are given in the following table.

Assume that the underlying distributions are normal and the population variances are equal. (a) Construct a 99% confidence interval for the difference between the mean weight of a new-process key and the mean weight of an old-process key. (b) Can you be 99% confident that the mean weight of a new-process key is less than the mean weight of an old-process key?