Question: Manufacturing and Product Development The mean weight of an ordinary key is an important consideration, as most Americans carry a pocketful of keys. A manufacturer claims that a new process produces a lighter and more durable key. Independent random 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, with the sample means and sample variances.
Assume the underlying distributions are normal and the population variances are equal.
a. Is there any evidence that the population mean weight of a new-process key is less than the population mean weight of an old-process key? Use a = 0.05.
b. Find bounds on the p value associated with this hypothesis test.